The substitute flicked home Marc-Antoine Fortune's low cross shortly after the former Nancy striker had levelled the scores.
Hibs had been heading for their second victory at Celtic Park this season after Anthony Stokes netted a penalty early in the second half.
But the late turnaround took Celtic 10 points ahead of Dundee United in second spot and prevents Rangers from being able to clinch the title against Hearts at Ibrox tomorrow.
The late struggle had not seemed likely when Robbie Keane netted his 13th Celtic goal in the fourth minute. Aiden McGeady's low cross from the left found Keane in space and the Irishman stroked the ball into the bottom corner from 12 yards.
Hibs levelled two minutes later though when Derek Riordan rifled a powerful 20-yard strike just inside the post after a positive run and lay-off from Stokes.
Colin Nish squandered a good chance to put the visitors ahead when he failed to connect with a ball across the six-yard line from Stokes.
Celtic soon had an even better chance when Keane played Niall McGinn through after good link-up play from Fortune, but Hibs goalkeeper Graham Stack got a crucial touch to divert the ball behind for a corner as the Northern Ireland winger tried to flick the ball home.
Stack held a deflected strike from Landry N'Guemo and Keane fired over after good skill outside the box as Celtic began to take control.
The hosts failed to keep the momentum going and Riordan fired over after being afforded space 25 yards out.
Wilson failed to hit the target from 20 yards before Fortune missed a good chance when he beat Hanlon to McGeady's cross but headed over from four yards.
Artur Boruc kept Celtic level in the 38th minute with a good one-handed save after Stokes had got away from his man in the right channel.
Celtic responded and McGeady's low cross just evaded Scott Brown before Ian Murray cleared inside the six-yard box, and Fortune fired just over after a good turn inside the box. Keane then saw an effort from the edge of the box deflect wide just before the break.
Fortune hit the outside of the post from a tight angle after his chance appeared to have been lost following Keane's lobbed through-ball.
But Hibs went ahead six minutes into the second half after a soft penalty award by Stephen Finnie, who ruled that Josh Thompson had caught Stokes with a high foot as the pair went for a bouncing ball. Stokes fired the ball into the bottom corner just out of Boruc's reach.
Celtic lost Darren O'Dea to injury with Andreas Hinkel coming on and Mark Wilson moving into central defence.
Celtic were struggling to get back into the game but the substitute threatened midway through the half with a low drive from 22 yards that was parried by Stack, before Sol Bamba got in front of Fortune to clear.
Celtic stepped up the pressure and Brown shot just wide from 20 yards before Morten Rasmussen had a strike parried from a tight angle after a clever lay-off from Keane.
Keane then shot inches wide from Fortune's cutback before Celtic equalised in the 80th minute. Stack blocked Keane's close-range effort following McGeady's low cross but Fortune tapped home the rebound.
Rasmussen shot inches wide from the edge of the box after Keane had set him up but the Dane was soon celebrating in the 87th minute.
The substitute got a toe to Fortune's low cross from the right to sneak the ball inside Stack's near post with manager Neil Lennon racing 30 yards to join the celebrations on the touchline.