Chelsea restore three-point lead
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.
Chelsea have 40 points, United 37 and Arsenal 32.
"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."
Chelsea, without injured top scorer Didier Drogba, dominated against opponents led by their own former manager Avram Grant, who was given a warm welcome by the home fans.
Nicolas Anelka put the Blues ahead in the 23rd minute in his 100th appearance for the club, slotting the ball into the bottom right corner past goalkeeper Asmir Begovic who started as a replacement for the unwell David James.
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.
With Chelsea in danger of squandering a golden opportunity, Lampard stepped up to lash home the 79th-minute penalty on his 300th league appearance for Chelsea.
Arsenal took the lead against the run of play with Cesc Fabregas, who limped off injured just before half-time, scoring with ease in the seventh minute after atrocious defending.
Andrei Arshavin hit the post before Burnley hit back when Graham Alexander scored from the penalty spot in the 28th minute after Thomas Vermaelen downed Cameroon midfielder Andre Bikey.
"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.
The Frenchman was also critical of the crammed calendar, with Arsenal back on the road after playing at Liverpool last Sunday.
"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.
Manchester City crashed 3-0 to fifth-placed Tottenham Hotspur at White Hart Lane, the ambitious northerners suffering only their second league defeat of the season after drawing eight of their last 10 games.