The win moved Saints up to seventh on a day when their play-off hopes were ended, with Huddersfield clinching sixth spot.
Southampton were unable to reproduce their spectacular Johnstone's Paint Trophy winning performance against the Cumbrians last month and struggled to make the breakthrough as they stuttered in front of goal, with Lambert unusually wasteful as he volleyed Antonio's teasing cross wide.
Antonio broke the deadlock a minute before half-time with a spectacular volley after Papa Waigo's cross picked him out at the far post.
But Carlisle levelled in first-half injury time through veteran defender Ian Harte, who curled home a delightful free-kick from 19 yards for his 18th goal of the season after Dan Seaborne rashly clambered all over Scott Dobie.
Antonio was the architect as Lambert put Saints ahead less than a minute into the second half, the winger providing the cross for the striker to clinically volley in his 34th goal of the season from a tight angle.
Saints wrapped up the points with a third six minutes later. Antonio's initial shot was charged down by Danny Livesey but Adam Lallana fed the ball back to Antonio, who skilfully tricked his way past Livesey to tuck his shot under Carlisle keeper Adam Collin.
Carlisle were gifted a second goal in injury time as a mix-up between Seaborne and Saints keeper Kelvin Davis presented the ball to Gary Madine, who rounded Davis and saw his shot bundled over the line by Saints defender Jose Fonte.