Lambert struck twice in the second half to take his tally to 17 for the season as Southampton continued their climb up the table.
In a dour first half, Tranmere keeper Luke Daniels was called into action to claw away Lambert’s powerful shot while the striker was also involved in the only other incident of note in the half when he was booked along with Tranmere defender Ian Goodison after a shoving match.
Southampton took just five minutes of the second half to take the lead, showing the sort of patience they lacked in the first period to open up Tranmere, with David Connolly laying a perfect pass into the path of defender Dan Harding who struck a sweet left-foot shot past Daniels.
Marlon Broomes’ needless handball gave Lambert the chance to score his 16th goal of the season from the penalty spot after 64 minutes.
Lambert topped off a fine afternoon with a stunning goal six minutes later, curling home a free-kick from 30 yards after Harding had been fouled.