David Nugent was clear on goal but saw his shot well saved by Petr Cech and then a Portsmouth counter-attack led by Peter Crouch ended with Niko Kranjcar shooting narrowly wide.
Drogba struck with a low shot from Jose Bosingwa's cross 12 minutes from time to give Chelsea its fourth consecutive victory by the odd goal since Guus Hiddink replaced Luiz Felipe Scolari as manager.
Before the game Portsmouth confirmed that Paul Hart would remain as manager until the end of the season, having taken over from sacked Tony Adams on a caretaker basis in February.
Liverpool went ahead seven minutes after the break against Sunderland when Steven Gerrard headed the ball across goal for Ngog to tap in his first Premier League goal.
The home side doubled its lead when keeper Marton Fulop made a meal of saving an overhead kick from Ngog and Benayoun, who scored the winner in the Champions League victory at Real Madrid last week, tucked in the rebound.
"I'm happy with the goal, but the most important thing is the points," Benayoun said.
"After we lost against Middlesbrough, it was important to come back to winning ways.
"We were very disappointed. We expected to beat Middlesbrough - but we did a job tonight."
Sunderland had spurned a great chance in the first five minutes, when Kenwyne Jones bamboozled defender Martin Skrtel, then outpaced Jamie Carragher but shot straight at Jose Reina.
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