Benjani struck a hat-trick as Portsmouth beat Reading 7-4 at Fratton Park.
The Zimbabwean forward scored twice in the first half and, although Stephen Hunt and Dave Kitson hit back either side of the interval to equalise, the hosts soon forged ahead again.
Hermann Hreidarsson restored Portsmouth's lead and, after David James had prevented another leveller by saving Nicky Shorey's penalty, Benjani and Niko Kranjcar made it 5-2.
Shane Long reduced the deficit but his strike was promptly cancelled out by Ivar Ingimarsson's own goal.
In stoppage-time, Sulley Muntari converted a penalty to make it 7-3, before Sol Campbell put through his own net to complete the scoring.
Portsmouth moved up to sixth with 12 points, while Reading slipped to 17th with seven points.
Luis Suarez scored a hat-trick at Carrow Road as Liverpool secured their first victory of the Premier League season at the sixth attempt.
Suarez struck twice in the first half and then set up a goal for Nuri Sahin before completing his treble and making it 4-0 in the 57th minute.
Steve Morison hit back for Norwich but Leon Barnett's own goal restored Liverpool's four-goal lead. Grant Holt scored a late consolation for the Canaries.
Liverpool leapfrogged their hosts in the table, jumping four places to 14th with five points. Norwich slipped into the relegation zone with three points.