The home side led through Andre Bikey after an inspired first half, but Chelsea struck back with two goals in three minutes early in the second period.
The quick-fire double was rough luck on Reading, who had earned a goalless draw at champions Manchester United on Sunday.
And the home side's misery was compounded late on when Kalifa Cisse saw red on his debut for a second yellow card.
Reading had made a fine start to the game and might have been in front inside two minutes when Nicky Shorey picked out John Oster at the far post, but the winger took too long and allowed Ricardo Carvalho to close him down.
Ivar Ingimarsson then headed wide after Stephen Hunt's corner had found him unmarked in the penalty area and Hunt was denied a certain goal when Tal Ben Haim took the ball off his toe after Kevin Doyle had headed back Oster's cross.
Reading suffered a blow on 29 minutes when former Chelsea defender Michael Duberry was forced to hobble out of the action, but it proved a blessing in disguise for Reading as his replacement opened the scoring with his first touch just seconds after coming on.
Ingimarsson's fine header from a Shorey delivery caused Petr Cech to flap at thin air and Bikey was on hand to bundle the ball into an empty net.
The home side were buoyant and Hunt was inspired. Despite picking up a booking for a foul on Paulo Ferreira, the spiky midfielder was everywhere and had the upper hand on his former Royals team-mate Steve Sidwell, who was booked on his first Chelsea start for a foul on Cisse and then substituted at half-time.
Chelsea looked at a loss as to how to handle the rampant home side, who nearly doubled their lead 10 minutes before half-time.
Hunt's back heel allowed Kevin Doyle to float a deep cross to the far post and this time Oster hit it first time only to see his effort smack against a post.
But Jose Mourinho gambled at half-time, replacing Sidwell and Ferreira with Claudio Pizarro and John Obi Mikel, having already used one substitute.
And the move paid off spectacularly as the visitors scored twice in the first five minutes of the second half to turn the match on its head.
Frank Lampard levelled, running into the space vacated by Bikey and holding off Shorey to slot past Marcus Hahnemann.
And Hahnemann was beaten again three minutes later when Shaun Wright-Phillips outstripped Shorey again and teed up last season's leading Premier League scorer Didier Drogba for a spectacular strike from the edge of the box.
Reading fought gamely but Hunt missed the chance for a dramatic injury-time equaliser when he completely missed his kick in a goalmouth scramble.