The Eagles would seemingly rue a spate of missed chances in the first half as Ricardo Pereira drew first blood for the Foxes, but an unfortunate Daniel Iversen own goal preceded a Mateta winner in the fourth minute of added time to kick off Hodgson's return in spectacular fashion.
A classic case of new manager bounce was clearly in effect at Selhurst Park, as a reborn Palace attacked the Leicester backline at every opportunity, albeit without the goal that their fans so craved.
Having survived an early onslaught, the Foxes made the woodwork rattle with 11 minutes gone - albeit in unintended circumstances - as Victor Kristiansen's cross-cum-shot intended for Kiernan Dewsbury-Hall struck the bar as Palace survived.
At the other end of the field, Iversen had no fewer than three saves to make inside the opening 20 minutes - with Wilfried Zaha consistently causing chaos on the left - and Timothy Castagne had to be alert to block the Ivorian's goal-bound effort in the 21st minute.
The blue and red shirts just kept on coming, but Brendan Rodgers's side dug incredibly deep to keep Palace at arm's length, and the Eagles suffered a heartbreaking injury blow just before the break.
Trying to connect with Jeffrey Schlupp's long ball on the stretch, Zaha appeared to tweak his groin and trudged off in tears to be replaced by Jordan Ayew, and Leicester's clean sheet remained intact as the half-time whistle blew.
Palace's 20 shots was the most for a Premier League side in the first half of a match since 2015, but Zaha's injury clearly had a major psychological effect on Hodgson's troops, as Leicester were immediately on the front foot at the start of the second 45.
The Foxes' endeavours would be rewarded in some style in the 56th minute, as Pereira broke the deadlock with a powerful drive into the top corner from Castagne's cross, but their lead was wiped out a mere three minutes later in unorthodox circumstances.
In similar fashion to Emiliano Martinez's own goal against Arsenal, Palace starlet Eberechi Eze's free kick struck the bar in the 59th minute, but the ball deflected into the net off an unfortunate Iversen.
Neither side was content with a point, but the game was ostensibly set to end with the spoils shared when Mateta missed a gilt-edged chance in the dying embers, but the Frenchman redeemed himself and then some.
With seconds remaining, Ayew - who had replaced the stricken Zaha - charged inside from the left and threaded a pass through to Mateta, who spun away from Harry Souttar and fired home low into the net to send the Palace faithful into pandemonium.
Palace remain 12th in the table on 30 points and are next in action away to Leeds United next Sunday, while Rodgers's men have dropped below the dotted line into 18th and host Aston Villa on Tuesday.