Van Gaal's men fully focused on Operation Wembley
Yeovil 0 Manchester United 2
The passion with which Manchester United celebrated their goals and ultimate victory over the League One's bottom club demonstrated how seriously they are taking the FA Cup.
Ander Herrera was even cautioned for his gleeful reaction to scoring, removing his shirt as he rushed towards the jubilant 2,149 away fans standing behind the goal.
Angel Di Maria confirmed the progress to the fourth round in the 90th minute, dinking the ball over Yeovil keeper Jed Steer as United's fans danced on the open terrace.
United seem on a mission, Operation Wembley, giving substance and direction to a strange season.
It said much for United's hunger for the Cup that their wing-backs, Rafael and Luke Shaw, both played through the pain barrier, finally coming off at the break to have injuries attended to.
"Rafael has a fracture of his bone so it was fantastic he had the guts to play through, but I have to change him, and also Luke Shaw had an ankle problem," said United manager Louis van Gaal.
Rafael left the ground early, driven to hospital.
Van Gaal, who rested the likes of Robin van Persie and Michael Carrick, is doing a good rebuilding job but he could do with a trophy to add lustre to his work.
United's manager reiterated his belief that they could overhaul Manchester City and Chelsea in the Premier League race but the Cup is surely a more realistic target.
United captain Wayne Rooney is full of motivation; he has never laid hands on the Cup, having joined three months after United's last triumph in 2004.
Ryan Giggs has already had a word with his boss about this season's holy grail, the hunt for a 12th FA Cup on May 30.
"I have heard off my fantastic assistant that United for 11 years have not won this FA Cup so maybe we can do that but it is a long way,'' said Van Gaal.
"The priority is also the Premier League but nine points is not so many.''
Van Gaal described the death-or-glory nature of Cup combat as "death or the gladioli" but it took United more than an hour to reach out and pluck the bloom from Somerset soil.
Yeovil delivered a resilient performance in keeping with their Cup traditions, pressing United relentlessly, and refusing to go quietly into the night as dusk settled on Huish Park in the second half.
They will reflect ruefully on a glorious missed chance by Kieffer Moore nine minutes into the second half with the score at 0-0.
Gary Johnson's men will also reflect that it took players who cost £29m and £59m respectively, Herrera and Di Maria, to break their hearts.
Yeovil respected their guests but were never in awe of them. When the captains were in the referee's room before kick-off, handing in team-sheets, Joe Edwards asked Rooney if he could have his shirt after the final whistle. Yet Edwards and his players played throughout as if believing they were equals.
For this was the day when the Cup came to town again, when the elite dropped in on Somerset, when locals briefly dreamed of another chapter in Yeovil's giantkilling legend.
From three hours before kick-off fans gathered outside Huish Park, some waving 'Manchester Who?' and 'We wanted City' banners.
Some broke away from their vigil waiting for the visitors' team bus to nip into the adjacent portable building selling thousands of old programmes, including United's most recent Champions League final appearances in Rome in 2009 and at Wembley 2011.
Rooney, who played in both games, was now stepping from those sepia-print pages, stepping from the bus and stepping out at Huish Park.
Outside, Yeovil fans were staring at Alex Ferguson's helicopter touching down in a nearby field.
Inside, an ambush was briefly plotted. Van Gaal needed all his managerial nous to get his players to break down Yeovil's resilience. "In the first half they gave no time to us on the ball, a lot of pressure,'' said Van Gaal, dismissing the notion that a Premier League side should automatically sweep aside a side rooted to the bottom of League One.
"It is not a matter of how far below (a team is),'' said Van Gaal.
"When you see their performance it was fantastic.
"Everyone thinks these players from United are €100m players against €5,000 players, but it is not like that. When you are organised like Yeovil, and you believe, they can be tough."
Edwards and Co were not standing on ceremony, certainly not standing off their distinguished guests.
Ben Nugent twice beat Radamel Falcao for a high ball. Simon Gillett hounded Shaw. Chased by Moore, Chris Smalling hoofed the ball out of the ground. Rooney and Falcao made headed clearances.
United knew they were in a scrap. Yeovil attacked every ball. Moore rose to meet a ball and clashed heads with Paddy McNair. Both continued with bandages.
Looking on were Edwards' family, all of them United fans, who postponed a skiing holiday to be here.
Edwards himself grew up wearing a 'Giggs 11' United shirt in kickabouts as a boy near Gloucester.
Relishing this opportunity against his idols, Edwards was buzzing around midfield, although going in with excessive force on Darren Fletcher.
Yeovil defended so well for an hour. Faced with Falcao tearing into the box, Stephen Arthurworrey timed his challenge perfectly, sliding in to nick the ball away.
The half could have been even more awkward for United had referee Craig Pawson spotted McNair's clear handball as Gillett threatened.
Yeovil were applauded from the field at the break and deservedly so. One of their supporters had flown in from Australia and his team were not letting him down, making light of their travails in League One.
Van Gaal made his move at the break, sending on Juan Mata and Jonny Evans, replacing Rafael and Shaw.
United now had a centre-back-four. "I changed the shape to 4-4-2 and we kept the ball better, had more patience,'' said Van Gaal.
After 54 minutes came what should have been a golden moment for Yeovil.
Evans inadvertently flicked on a cross to Moore, who chested the ball down with De Gea's goal at his mercy.
The fans in the Thatchers Gold Stand leaned forward, willing Moore to score. His right boot came down and connected with the ball, not strongly enough and David De Gea was able to collect easily. Moore looked to the skies in frustration. What a chance.
Such were United's struggles that Van Gaal twisted for the final time, sending on Di Maria for Falcao after 59 minutes.
Within five minutes, United were ahead. Rooney cut the ball in from the left, and Fletcher helped it forward. The ball clipped Gillett and fell sweetly for Herrera, who had done little all game but reacted brilliantly here.
As the ball dropped, Herrera caught it magnificently, sending it flying in over Steer to the unrestrained joy of the United fans standing behind the goal.
"Herrera's goal was class,'' said Van Gaal.
But Yeovil remembered their Cup DNA. Edwards had a powerful header cleared by Di Maria. Moore's shot deflected wide off Smalling.
Rooney tracked back to intercept a cross from Nathan Smith, who had been a genuine threat down Yeovil's left.
Yeovil were inevitably vulnerable on the break and on the cusp of full-time, Rooney elegantly slipped a pass to Di Maria, who raced 50 yards and dinked the ball effortlessly over Steer.
Di Maria did his heart-shaped celebration with his fingers, not only sending his usual message to his loved ones but also pointing out United's quickening passion for the FA Cup. (© Daily Telegraph, London)