The striker tucked away a 59th-minute penalty after Danny Coles had fouled Lee Barnard. By then the Saints were already two up and coasting in Saturday's League One clash.
Defender Jose Fonte volleyed them ahead from a 10th-minute corner and Adam Lallana doubled the advantage with a close range finish after Dean Hammond's 34th minute shot had found him unmarked in front of goal.
Barnard completed the rout by firing in off the crossbar in injury time and Rovers fans chanted "what a load of rubbish" at their team.
They were outplayed for long periods, but Coles went close with a 31st-minute header, brilliantly saved at full stretch by Kelvin Davis, and Gary Sawyer saw a 73rd-minute volley hit the angle of post and crossbar.
Will Hoskins also shot just wide as Saints coasted through the closing stages, having established their superiority long before.
Lambert received a huge ovation from all sides of the ground when substituted 11 minutes from time. The former Rovers man remains hugely popular at the Memorial Stadium.