England international Welbeck, who was making his first appearance since April 2015 for the Gunners after a serious knee injury, headed home in the fifth minute of added time at the Emirates Sunday after coming on as a late substitute.
Arsenal's north London rival Tottenham Hotspur also boosted its hopes later Sunday with a battling 2-1 win at fourth-placed Manchester City, both teams closing to within two points of leader Leicester with 12 games remaining.
Leicester, down a man after the 54th minute dismissal of defender Danny Simpson for a second yellow card in quick succession, had looked set to hold out for a 1-1 draw to maintain the five-point lead it held going into the crucial fixture.
But in the last action of the match, substitute Marcin Wasilewski conceded a needless free kick and Mesut Ozil's free kick was glanced home by Welbeck, who has spent a frustrating 10 months on the sidelines.
He had missed an earlier chance after coming on as an 83rd minute replacement for Alex Oxlade-Chamberlain, but made no mistake this time.
"Dying seconds, we kept pushing, had chance after chance," Welbeck told Sky Sports.
"I missed the first opportunity and tried to make amends. It is important and the most important thing is to get the win.
"It has been a rollercoaster for me, a difficult moment, and my family and friends know what I have been through."
It was heartbreak for unheralded Leicester, which took the lead just before halftime after Nacho Monreal tripped Jamie Vardy.
The striker, so prolific for the Foxes in their unlikely title bid, got up to drive the ball past Petr Cech from the penalty spot.
Arsenal felt hard done by after its earlier penalty appeal when Oxlade-Chamberlain's cross into the box was blocked by the arm of N'Golo Kante was rejected by referee Martin Atkinson.
Leicester goalkeeper Kasper Schmeichel also had to be smart to keep out Aaron Ramsey, who was played through one on one, but Cech was also called into action to brilliantly keep out a Vardy header.
However, Leicester's hopes of victory took a nosedive when Simpson pulled back Oliver Giroud to be shown red by Atkinson.
Claudio Ranieri's men still led until the 70th minute when Theo Walcott, also a substitute for Francis Coquelin, smashed the equalizer after good work by Giroud.
It was all Arsenal now, but with Leicester showing the resilience which has so impressed this season, until Arsene Wenger threw on Welbeck and he repaid his faith.
"It will strengthen our belief that we are in the fight," said the Frenchman.
Tottenham is also firmly in the fight, second on goal difference ahead of Arsenal, with Manchester City a further four points adrift after another chastening home defeat, having lost 3-1 to Leicester last weekend.
Tottenham had the better of the first half without threatening Joe Hart's goal, but went ahead after the break as Raheem Sterling was adjudged to have handballed Danny Rose's cross in his own penalty area.
Referee Mark Clattenburg waved away the protests before Harry Kane stepped up to strike home his 15th goal in his last 17 EPL games.
The perceived injustice sparked City's best period and after a spell of pressure home substitute Kelechi Iheanacho equalized with a sweet strike after a cut back from Gael Clichy.
But rather than the home side pushing on for three points, it was Tottenham which retook the lead, another substitute, Eric Lamela, playing a key part as he cleverly found Christian Eriksen, who slotted his shot under Hart in the 84th minute.
A fingertip interception from Hugo Lloris denied City an equalizer at the death, Manuel Pellegrini's men suffering a real setback in its bid for a second English championship crown in three years.
Sunday's other game saw Liverpool rout bottom club Aston Villa 6-0 at Villa Park, with Welbeck's fellow injury-blighted international teammate Daniel Sturridge also scoring on his return to club action.
Sturridge gave his side a 15th minute lead with James Milner, Emre Can, Divock Origi, Nathaniel Clyne and Kolo Toure also on the scoresheet for Jurgen Klopp's rampant lineup.