Allardyce had looked as though he would have to settle for a deeply uninspiring stalemate in Trnava - the hosts having held firm in the World Cup Group F qualifier despite Martin Skrtel’s sending-off after a nasty stamp on Harry Kane.
However Lallana picked a perfect moment to break his international duck and seal a 1-0 success.
The Liverpool forward had already clattered the post when the ball broke for him inside the area, with seconds of the four added minutes left.
He showed neat footwork and got his shot away, then turned away in celebration as Matus Kozacik let the ball squirm between his legs and over the line.
The victory will be a huge tonic for Allardyce, and buys him a little extra time in his honeymoon period, but he will have seen plenty of familiar shortcomings.
Wayne Rooney, on the occasion of his 116th cap - beating David Beckham’s England outfield record - again looked confused and inconsistent in a midfield role many thought he would never play again, Raheem Sterling struggled for end product and Harry Kane was once more worryingly lethargic up front.
Allardyce has bags of enthusiasm for the task at hand and although he does not have a magic wand, he will be happy to head back with three points in the bank.
England began by probing the flanks, Danny Rose and Kyle Walker pushing high up the field, but there was a disjointed feel from an early stage.
Rooney was on corner duty and that seemed the only way to get the captain into the final third, as he frequently dropped even deeper than Eric Dier and Jordan Henderson in midfield.
At one stage, just after the half-hour mark, he was the only outfield player in the England half.
Rooney never shirked from the spotlight, demanding possession more than any other player, but at that stage his attempts at playmaking - notably a couple of ambitious cross-field passes - were simply not good enough.
Joe Hart is another player who has been under the spotlight and when he received a return pass from Gary Cahill in the seventh minute he had the perfect chance to show Manchester City boss Pep Guardiola he was wrong about his distribution.
Instead Hart scuffed his kick to a Slovakian shirt and was forced to scramble back to his line in anticipation of a shot that never materialised.
England’s first chance of note took 22 minutes to arrive, Kane failing to get a proper connection on Walker’s low near-post cross, in what was his only real sight of goal.
Their only other serious effort before the break came when Sterling took advantage of a ponderous clearance and dragged wide from 10 yards.
Slovakia showed glimpses in response, Jan Gregus running out of room after outmuscling Henderson and giving John Stones the slip.
A Rose error gifted them a good chance in the 37th minute but the stretching Dusan Svento could not reach Michal Duris’ drilled pass.
By half-time England had settled into a pedestrian pace but Allardyce declined to immediately mix things up from the bench.
Instead, the game-changing moment came from Skrtel.
Even if he had not been booked for an earlier elbow, his stamp on Kane was a crass act, worthy of a red in its own right rather than the second yellow that was shown.
The home fans reacted with fury, despite it being an open and shut case, and the audible rise in decibel levels raised the sense of occasion.
Dele Alli’s arrival upped the ante for England, the Tottenham man troubling Slovakia from the off with some neat touches and a sense of vim and energy otherwise lacking.
His introduction almost coaxed some life out of Spurs team-mate Kane too, but he faded again and gave way late on to Daniel Sturridge.
England were on the charge for the final 20 minutes and Lallana almost broke the deadlock with an opportunistic drive that beat the goalkeeper but rebounded off the inside of the near post.
Theo Walcott, on for Sterling, might have done something with the rebound but could not bring it under control.
There were other chances - or half-chances - Rooney with the first official shot on target with a low effort that nearly took Kozacik by surprise, but the moment seemed to have passed.
Having not netted in his first 26 England appearances, Lallana finally found a finish and for Allardyce, celebrating passionately on the touchline, the timing was perfect.