It did appear that Slovakia had done enough to frustrate the Three Lions once again following their stalemate at Euro 2016, but Lallana won it in the fifth minute of stoppage time to ensure that England started Group F with a win.
News of Allardyce's first England XI broke on Friday and there were no late changes to the team as Wayne Rooney won his 116th cap, making him England's most-capped outfield player. The Manchester United forward skipped a side that also included new Torino goalkeeper Joe Hart.
Harry Kane, Raheem Sterling and Jordan Henderson were also given starting roles, while it was John Stones alongside Gary Cahill in central defence, leaving Chris Smalling on the bench after starting the season out of the Man United side.
As for Slovakia, head coach Jan Kozak made five changes to the team that lost to Germany in the last-16 stage of Euro 2016. In came Tomas Hubocan, Viktor Pecovsky, Jan Gregus, Robert Mak and Dusan Svento, but experienced pair Martin Skrtel and Marek Hamsik kept their spots in the XI.
It was a bright and open start to the Group F clash as both teams committed players in the final third, with Kyle Walker given licence to attack for England and Slovakia causing some issues down their right in the space vacated by Danny Rose.
Twice Slovakia had opportunities to deliver dangerous free kicks into the England box as play developed, but Cahill and Kane were on hand to produce two excellent clearances as the home side threatened the opening goal.
Kane was presented with the game's first real opportunity in the 22nd minute courtesy of a cross from Walker, but the Tottenham Hotspur forward had a fresh-air shot as his goal struggles this season continued.
Slovakia had a golden chance to make the breakthrough 10 minutes before the end of the first period when Michal Duris robbed Rose of possession before delivering a low cross towards Svento, but the midfielder just could not make contact.
Moments later, Sterling came close for England following a mix-up inside the Slovakia box, but the Manchester City attacker fired wide of the far post as it remained goalless at the end of the first period.
Sterling made a bright start to the second period as the Man City attacker delivered a dangerous cross towards Kane two minutes after the restart, before having a powerful strike deflected wide of the home side's post.
Henderson then struck one from distance as England continued to dominate in the early stages of the second half, but his effort cleared the target as Matus Kozacik remained untroubled between the sticks.
Skrtel was fortunate to escape a second yellow card in the latter stages of the first half for a foul on Kane and that was again the case in the 52nd minute as the centre-back hauled Kane to the deck in a wide position.
Skrtel did not escape five minutes later, however, as the former Liverpool defender was given a second yellow card for a stamp on Kane, which could have brought a straight red from the referee.
England continued to dominate the possession as the final 25 minutes approached and Kozacik had to make a smart save from Rooney, before tipping a Sterling effort over the crossbar during a period of pressure from the visitors.
Dele Alli and Theo Walcott were both introduced by Allardyce as the visitors looked to make the breakthrough and Lallana hit the post in the 76th minute before drawing a save from Kozacik as it somehow remained all square.
Daniel Sturridge for Kane was England's final change of the night and the Liverpool striker had a golden chance to win it five minutes from time when Walcott delivered a stunning cross towards the far post, but the substitute poked wide, before Lallana missed the post from distance.
The pressure continued into the latter stages and Walcott had a goal disallowed for offside, but eventually the breakthrough came in the 95th minute when Lallana found a route through the goalkeeper's legs after working a yard of space inside the box.
Next up for England is a home match against Malta on October 8, while Slovakia, who will expect to battle for first place in this group, will travel to Slovenia on the same night.