Ivory Coast international Drogba had put Chelsea ahead with a header from a Frank Lampard corner seven minutes before half-time but Leroy Lita, rejected by Chelsea as a teenager, levelled in the 67th minute with a diving header from close range after a cross from Glen Little.
Less than five minutes later, Drogba restored Chelsea's lead when he headed in a curling centre from Shaun Wright-Phillips.
Then, in the 85th minute Reading were level thanks to a bizarre own-goal. Chelsea and England full-back Ashley Cole's hurried clearance hit team-mate Michael Essien and went past keeper Hilario.
Ronaldo 'super sub'
Despite starting the match of the bench Cristiano Ronaldo scored twice for the second successive match to help Manchester United extend their advantage over Chelsea.
The Portuguese international was on the scoresheet barely a minute after coming on as a substitute at the start of the second-half, heading in a Paul Scholes corner.
Four minutes laters he made it 2-0 after South Korea's Park Ji-Sung was brought down in the box by Gary Teale for a penalty. The spot-kick was parried by Wigan keeper Chris Kirkland but Ronaldo scored from the rebound.
Ole Gunnar Solskjaer added a third goal on the hour mark before Wigan's Leighton Baines scored a penalty in the closing seconds.
|Benni McCarthy, left, pushed Liverpool out of third |
place and gave Blackburn a 1-0 win [AFP]
Liverpool, who started the day in third place, dropped down to the table after Benni McCarthy gave Blackburn a 1-0 win at Ewood Park.
"We had a lot of clear chances but we didn't score. If you miss these opportunities and you make a mistake then you will be punished," Rafael Benitez, the Liverpool manager, said.
Mark Hughes, the Blackburn manager, praised the South African striker.
"Benni was great today. While he's adjusting to the Premiership he's still scoring goals," Hughes said.
Gunners go third
Arsenal struggled against bottom-of-the-table Watford but ground out a 2-1 win to take them into third place.
Brazilian Gilberto Silva had put Arsenal ahead after 19 minutes with a header but Tommy Smith equalised just four minutes later with a close-range finish past Jens Lehmann.
Watford played enterprising football and fristrated the Gunners but Robin van Persie's late winner means they are still nine points from safety.
Bolton, Portsmouth and Tottenham all stayed in the hunt for European football next season with 2-1 wins over Newcastle, West Ham and Aston Villa.
Bolton made it four wins in a row after coming from behind to end Newcastle's recent revival.
Kieron Dyer put Newcastle in front only for Peter Ramage to head an own goal to put the home side level. Former France international Nicolas Anelka then pounced to score his sixth league goal of the season.
Defender Linvoy Primus scored with two headers before the break, his first goals since Boxing Day 2004, to give Portsmouth a 2-0 lead.
|Jermain Defoe scored a double against|
Aston Villa [AFP]
Teddy Sheringham's pulled one back for West Ham late on but couldn't prevent new manager Alan Curbishley suffering his first defeat as West Ham remained in the bottom three.
Jermain Defoe and Dimitar Berbatov combined for both of Spurs' goals before Gareth Barry got a consolation for Villa.
Elsewhere, Stephen Ireland's 78th minute goal for Manchester City, his first for the club, secured a 1-0 win away over fellow strugglers Sheffield United while the match between Everton and Middlesbrough ended in a goalless draw.