Written off as relegation certainties before a ball had been kicked, Wigan proved they are in no mood to be pushovers and the champions will happily vouch for that.
A draw was the least Paul Jewell's side deserved as they gave Chelsea the fright of their lives, particularly in the first half.
But their luck was out eight minutes from time when winger Gary Teale whipped in a terrific cross from the right. Damien Francis arrived unmarked to power in the header, but he could only look on in dismay as it clipped the crossbar.
And in stoppage time, Swedish midfielder Andreas Johansson dragged one chance wide and looped another over the bar.
Then with seconds left, Crespo seized his chance, beating Mike Pollitt with a terrific shot to clinch the points.
Wigan showed no sign of an inferiority complex as they carved out two top-class early chances to set the mood for a fearless and confident opening 45 minutes.
Record signing Henri Camara, snapped up from Wolves for £3.1million, tested keeper Petr Cech with a fierce left-foot strike and skipper John Terry did the mopping up, blocking the follow-up from Jason Roberts.
The speedy Camara was in the picture again, trying his luck with his right foot but the shot flashed just inches wide.
Chelsea were restricted to half chances with Didier Drogba hammering over the bar from just outside the box and Eidur Gudjohnsen also failing to hit the target.
Dutch ace Arjen Robben should have done better after beating Leighton Baines as he ran into the box but then fired wide.
Wigan had a great chance after 23 minutes when Francis and Camara combined to set up midfielder Alan Mahon.
The ex-Blackburn star had a clear sight of the target but failed to produce the finish, shooting over the bar after opting to use his favoured left foot.
Chelsea went agonisingly close from a Damien Duff corner. Terry beat Wigan captain Arjan de Zeeuw to the header but it flew just over the bar with Pollitt a very relieved spectator.
But Pollitt - a bargain £200,000 signing from Rotherham - came to the rescue two minutes before half-time, getting down low to keep out a goalbound shot from Duff.
Looking for inspiration, Chelsea made a double switch sending on Joe Cole and Shaun Wright-Phillips for Robben and Gudjohnsen.
Crespo then took over from Duff and as Chelsea piled on the pressure, the Argentina international was quickly in action forcing the save from Wigan keeper Pollitt.
The Latics failed to cash in when Jimmy Bullard hit a free-kick wide from the edge of the box and Chelsea again threatened when Cole tested Pollitt.
De Zeeuw, who had a magnificent game on his return after three years at Portsmouth, also chipped in with a timely challenge on Drogba to deny the £24million man a chance of glory.
Chelsea had a penalty appeal for handball against Teale turned down by referee Mark Clattenburg, but Crespo's late, late strike settled it.