With second-placed Manchester United visiting Tottenham Hotspur on Sunday, City stretched their lead as an own goal from Gretar Steinsson and a Mario Balotelli effort sealed their 19th successive home league victory.
Arsenal have not been in the title race all season but strengthened their claims for a top-four finish with Robin van Persie striking twice in a 2-1 triumph at Liverpool.
Van Persie's stoppage-time winner was his 31st goal of the season in all competitions and helped Arsenal move three points ahead of fifth-placed Chelsea who were beaten at West Brom by a late Gareth McAuley goal.
Roberto Mancini's team went in front after 23 minutes against Bolton when a shot by defender Gael Clichy took a big deflection off Steinsson.
Villas-Boas's side produced another lacklustre display which will again fuel media speculation about the Portuguese manager's future.
Frank Lampard wasted a glorious late chance for the visitors after McAuley's scrappy 82nd-minute goal had put West Brom in front.
"It was not good enough by Chelsea's standards," Villas-Boas told Sky Sports. "West Brom were far superior and we have to do much better."
"It means a lot to score at Anfield," said Van Persie after netting at the ground for the first time.
"We're proud of the win but I don't think we deserved it if I'm honest. Liverpool played better but to nick it at the end is pleasing."
Kuyt's spot-kick and immediate follow-up effort were both brilliantly saved by Polish goalkeeper Wojciech Szczesny who was in inspired form throughout.
