At last, Liverpool have discovered the existence of life without Luis Suarez.
First Johnson, a West Ham academy product a decade ago, silenced Upton Park for the third time here, unleashing one of his customary outside-the-area specials into the top corner.
Then Cole, shrugging off his pedestrian first half, paused for a split-second on his left foot before angling his finish beautifully beyond Jussi Jaaskelainen.
Finally, with a little help from the outstretched boot of James Collins, Jonjo Shelvey, once a West Ham youth player and a fan of the home club from the cradle, made it a triumvirate of former claret-and-blue assassins.
Shelvey, naturally desperate to impress in the absence of the suspended Suarez, was claiming the winner as his own.
In Liverpool's 15 league matches to this point, Suarez had scored 10 of their 19 goals and created another two of them.
The imperative to find an able deputy was glaring, and manager Brendan Rodgers was gushing about Shelvey's contribution.
"You see young Jonjo, at 20 years of age, playing the No 9 role in a different way, combining with the midfield players. I thought the kid was outstanding, especially as people are trying to compare him with Suarez."
This sounded suspiciously like a way of burying Liverpool's deficiencies for the first 75 minutes by trumpeting their resurgence in the final 15.
For there should still be no understating the club's predicament. While disciples might argue that they lie only four points adrift of the top four, the same could equally be said of Norwich, Swansea and Stoke. Such is the intensity of mid-table jostling that Rodgers' players remain just a couple of defeats from a relegation scrap.
The cold reality, as owner John W Henry keenly appreciates from a freezing New England, is that the team have won just five of 16 league games.
For this season at least, Henry and Fenway Sports Group have hitched their wagon firmly to Rodgers.
One senses that so long as the young manager produces a top-eight finish for Liverpool, coupled with a respectable Europa League run, he will be safe.
But the aspirations at such an august institution could, and should, be far greater.
Rodgers is never shy of acknowledging this, but as he spelt out his credo his words were less those of an inspiring philosopher than of a mightily relieved man.
"This is a unique club," he said. "To be the manager is an incredible pleasure.
"But you have to create that spirit, it doesn't just happen. It comes from working hard, developing, learning. Just keep moving steadily. We want to keep making progress, building our game, enhancing the structure of the team and the club. That's there for everyone to see."
It is a moot point. Liverpool started superbly, as Johnson signalled their intent with his 11th-minute missile, but from there they sank into a peculiar funk.
Rodgers, perhaps, put it best: "In the last 20 minutes of the first half we stopped playing." Allen's anonymity lasted long enough for West Ham to strike back, as the midfielder conceded a penalty by blocking Guy Demel's volley with his hand.
Mark Noble stroked the ball in from 12 yards with aplomb, even if there was scant fluidity in open play. It was perhaps in keeping with the game's disjointedness that the home side's second should have come courtesy of an own goal. A swift free-kick was passed to Matt Jarvis on the left, before Steven Gerrard arrived at the scene first to put the ball through his own net.
West Ham were in the ascendant, but the balance of the game tilted upon a serious injury to Mohamed Diame, their most creative force.
Raheem Sterling found the perfect deadweight pass for Cole, who contrived an elegant shot in front of goal to beat Jaaskelainen. Then Shelvey, seizing upon a dangerous cross from Jordan Henderson, pounced at the near post, even if the luckless Collins had the final touch.
"It was a bizarre game in many ways," Allardyce reflected. "I wouldn't have expected there to be five goals. You know that without Suarez, Liverpool don't score many." After a late salvo by the Suarez stand-ins, that wisdom might have to be revised. (© Daily Telegraph, London)