On the ropes against the Blue Square Bet Premier outfit, who had laid siege to the Liverpool goal as Rodgers' players defended their first-half lead, Suarez's handled goal within four minutes of entering the action tainted the Merseysiders' progression to a fourth-round tie against Oldham at Boundary Park later this month.
Despite the Liverpool manager's post-match assertion that Suarez's handball was not deliberate, the Uruguayan certainly gave the ball a fair whack with his right hand before beating goalkeeper Alan Marriott from close range.
Just as it would be utterly unrealistic to expect Suarez to do what Diego Maradona and Thierry Henry never did by telling the referee that the goal had been scored with his hand, it was also no surprise to hear chants of "cheat, cheat, cheat," raining down from the stands inside Field Mill.
Robbie Fowler might have urged the referee to backtrack on a penalty award during a game against Arsenal at Highbury in 1997, but that was a one-off in a hard-bitten profession where any inch is taken to claim a mile.
Suarez, a 54th-minute replacement for £12m debutant Daniel Sturridge, put the game beyond Mansfield when he palmed the ball down and then kicked it into the net on 58 minutes.
Referee Andre Marriner, having looked across at his linesman Mike Mullarkey, awarded the goal, despite the appeals of the incensed Mansfield players, led by Marriott.
Mansfield's anger was fuelled by their team having a penalty claim turned down moments earlier when Matt Green's backheel was blocked by a stray Liverpool arm on the goal line.
With tensions running high, a supporter wearing a blue and yellow jester's hat then ran onto the pitch and approached Suarez before being ushered away by stewards.
Whether Suarez's handball was deliberate or not, it took the shine off a stirring cup tie, during which Mansfield belied their status as a mid-table non-league club lying 93 places behind their illustrious opponents.
Having insisted prior to the game that he would be taking the tie seriously, Rodgers opted to make eight changes to his starting line-up, with the likes of Steven Gerrard, Glen Johnson and Daniel Agger given a day off altogether.
Suarez, meanwhile, was named on the bench, with Rodgers perhaps mindful of the need for a 'just in case' option should the game go badly for Liverpool.
When Sturridge put Liverpool ahead inside the opening 10 minutes, though, it appeared as though Rodgers' bold selection was justified after all.
Having gone close moments earlier when Suso sent a 25-yard effort flashing over the crossbar, Liverpool went ahead when Sturridge recorded his first goal for the club with a crisp finish on eight minutes.
At that stage, it appeared as though Mansfield were destined for a brutal dose of reality against the five-time European champions.
But Paul Cox's team overcame their nervous start and began to push Liverpool back, taking advantage of the uneven Field Mill pitch and Geohaghon's long throw-ins, which were straight out of the Rory Delap guide to causing defensive panic.
Liverpool still carried plenty of threat, with the impressive Shelvey linking well with Sturridge, but their failure to score a second injected Mansfield with energy and belief and they were unlucky not to equalise during a vibrant start to the second half.
Within the space of three minutes, Anthony Howell saw a close range shot saved before the same player was denied by the out-stretched leg of Jamie Carragher.
As Mansfield heaped pressure on the Liverpool goal, Louis Briscoe forced Jones in another save before the Australian 'keeper palmed away another effort from Clements.
But the goal just would not come, even when Geohaghon's downward header was saved and Green saw his backheel from two yards pushed away by the besieged Jones.
Having seen his team go close to conceding, Rodgers made the change which ultimately decided the game by introducing Suarez in place of Sturridge.
And within minutes, Liverpool's talisman did what he been sent on to do by doubling his team's lead.
Mansfield responded well, though, and the goal they deserved came on 79 minutes when Green beat Jones from 12 yards with a half-volley from Lee Beevers' cross.
It teed up a rousing finale, with more throw-ins from Geohaghon causing consternation in the Liverpool penalty area and Green testing Jones once again.
But Liverpool held on. Just. (© Daily Telegraph, London)