Nacho Monreal - who netted in Arsenal's FA Cup semi-final victory over Manchester City last time out - continued his form in front of goal when his 86th-minute strike deflected in wickedly off Leicester's German defender.
It was a relief for the home crowd following a lacklustre display from Wenger's men, who, despite desperately needing to make up ground on the teams above them, had been found wanting throughout at Emirates Stadium.
Alexis Sanchez epitomised Arsenal's performance with some sloppy touches and slack passing, though the former Barcelona winger still went closest for the hosts in a tepid first half - hitting the woodwork with a blistering strike on the stroke of half-time, with Riyad Mahrez having tested Petr Cech at the other end.
The Chile international is certain to come in for criticism after going down clutching his face in the final moments, a throw-in from close range having struck his shoulder.
Never in Wenger's 20-year tenure have Arsenal, who face title-challenging Tottenham next, missed out on a Champions League qualification spot, but they looked set to be held by Leicester until, with just over four minutes remaining, Huth's misfortune sealed the points.
The victory moves Arsenal up into sixth place, three points behind Manchester United and four adrift of fourth-placed City, with Jose Mourinho and Pep Guardiola's sides facing each other on Thursday.
29 - Arsenal have now scored 29 league goals in the final 30 minutes of games in the Premier League this term; the most of any side. Drama.— OptaJoe (@OptaJoe) April 26, 2017
A hero against City, Sanchez almost turned into the villain for Arsenal when he conceded possession deep in the hosts' half, but Jamie Vardy could not apply the finish.
Though Arsenal dominated the ball, they lacked any verve or guile in the opening stages, and only a fine Cech save from Mahrez's venomous half-volley denied Leicester the lead 20 minutes in.
Cech's counterpart Kasper Schmeichel was called into action soon after, reacting sharply to keep out Theo Walcott's effort, with Monreal also going close.
Leicester weathered the storm, though, and Mahrez went close again at the culmination of a fantastic solo run - sending a low effort crashing into the side-netting from an acute angle.
Sanchez continued to cut a frustrated figure up top as half-time approached, but he was just inches away from giving Arsenal the lead when his dipping strike rattled the crossbar.
Leicester had Huth to thank 10 minutes into a rather tepid second half, the former Chelsea man diving in brilliantly to prevent Sanchez getting through on goal.
Sensing an opening, Arsenal upped the tempo - Granit Xhaka forcing Schmeichel into action with a deflected strike from 25 yards out before Laurent Koscielny squandered a close-range header.
Danny Welbeck netted a dramatic winner in the corresponding fixture last season, and the England man almost set-up Sanchez immediately after coming on as a substitute.
But for all Arsenal's attacking talent, it was defender Monreal who created the winner - his first-time strike finding the bottom-right corner courtesy of a huge deflection off the unfortunate Huth.
Key Opta stats:
- Arsenal extended their unbeaten run over Leicester in the Premier League to 21 games (W14 D7), not losing since their very first meeting in November 1994.
- The victory saw the Gunners equal their longest home winning streak against a single opponent (10 successive wins against Everton between January 1997 and September 2005).
- Leicester have won just one of their previous 19 away games in the Premier League (D6 L12).
- Jamie Vardy became the 10th player to reach 100 Premier League appearances for Leicester City, while his first in the competition was also against Arsenal (in August 2014).
- Arsenal have now scored 29 league goals in the final 30 minutes of games in the Premier League this term; the most of any side.
- The Gunners have also netted more second-half goals in the Premier League than any other team this season (40).
- For Leicester, meanwhile, this was the first time they have failed to score in a Premier League game under Craig Shakespeare – they had netted at least twice in each of the previous seven beforehand.
- No player has scored more own goals than Robert Huth in the Premier League this season (2).