Villa had lost their opening two matches in the Premier League but an influential display by midfielder Stephen Ireland ensured League One Tranmere failed to spring an upset.
He played a part in the build-up to the opening goal from Delph after 38 minutes and set up the second for Herd mid-way through the second period before Bent added a third.
Lambert made six changes from the side beaten at home by Everton on Saturday but his reshuffled line-up comfortably had the better of a side unbeaten in their opening three league matches.
It was just the confidence boost Villa needed ahead of Sunday's next league outing at Newcastle although Lambert will have hoped to have bolstered his squad before the trip to the north east.
Lambert is reported to be lining up a bid for Middlesbrough defender Joe Bennett after Villa had an offer for Genk striker Christian Benteke rejected today.
Tranmere were the first to threaten after a mistake by Villa midfielder Barry Bannan allowed Andy Robinson to thread the ball through to Jean-Louis Akpa Akpro but his shot was blocked.
Villa defender Nathan Baker bundled the ball over the line from a Bannan free-kick after 19 minutes but his effort was ruled out for an infringement.
Tranmere defender Ash Taylor became the first player to be yellow carded after 28 minutes for holding Bent as he tried to run onto an Ireland through ball.
Bannan curled the resulting free-kick over the defensive wall and it clipped the crossbar with Williams well beaten.
Villa were creating more opportunities and Williams blocked a low drive from Bent with his feet after more good play by Ireland.
It came as no surprise when Villa went ahead after 38 minutes with Delph making no mistake at the far post after a cross from debutant Enda Stevens was not cleared.
Ireland shot over after being teed up by Bent as Villa looked to press home their superiority.
Tranmere showed plenty of purpose at the start of the second period and Liam Palmer's fierce attempt was blocked by Nathan Baker.
Villa returned to the offensive but Ireland failed to take advantage of a promising position inside the box when he tried to pick out Bent instead of shooting himself.
The former Manchester City player played in Andreas Weimann but Williams was the equal of his shot on the turn.
Weimann then headed just over from an Eric Lichaj centre before Villa doubled their lead after 66 minutes.
Ireland was the creator after a run to the by-line and his low cross was parried by Williams to Herd who made no mistake from close range.
Williams turned aside a curling Ireland effort before Bent made it 3-0 with 10 minutes left when he converted a pull back from Brett Holman for his first goal of the campaign.