Champions Manchester United had pulled level on points after beating a weakened Wolverhampton Wanderers 3-0 on Tuesday in manager Alex Ferguson's 900th league game in charge.
Arsenal failed to match the pace, held 1-1 by a spirited Burnley at a rain-lashed Turf Moor to move ahead of Aston Villa on goal difference in third place with a game in hand but eight points off the lead.
"It was hard work," Chelsea manager Carlo Ancelotti told Sky Sports News.
"After four games without victory...we didn't have confidence. We did a good job, not a beautiful job but a hard job and this is important."
Portsmouth refused to give in and were rewarded six minutes after the break when Jamie O'Hara's free kick hit the wall and fell for Frederic Piquionne to smash the equaliser into the roof of the net.
"I am disappointed with the point," said Arsenal manager Arsene Wenger, who ruled Fabregas out of Saturday's home match against Hull City. "It was a Cup game and the pitch was very difficult tonight.
"You do not travel two times in three days with the intensity of these games without paying for it," he said.
Liverpool, marking the 50th anniversary of the late Bill Shankly taking over as the club's manager, grabbed a morale-boosting 2-1 win over Wigan Athletic at Anfield to move ahead of Manchester City into sixth place.
David Ngog broke the ice for Liverpool in the ninth minute and Fernando Torres came off the bench to make it 2-0 before Charles N'Zogbia netted in injury time for Wigan.
