As a consequence, Walsall's six league-game unbeaten run was brought to a halt, but they could not be faulted for effort and were the more lively side in the opening 15 minutes during which Mark Bradley hammered one shot over the bar and Troy Deeney saw a shot deflected into the side netting.
Byfield also clipped the far post with a header on 11 minutes, but Southampton then took over, surging ahead in the 32nd minute when a lovely through-ball from Lloyd James saw Connolly out-strip the home defence and drive in his sixth goal for the club.
Before Walsall could gather their thoughts, Dean Hammond struck a second on 38 minutes when a deflected shot from Connolly landed at his feet.
In the second half, the Saints made sure of the points in the 65th minute, Connolly setting up top scorer Rickie Lambert. A minute later, Byfield bagged his ninth of the season for Walsall to register number 100 of his career, but Southampton stood firm after that.