In-form striker Tammy Abraham broke the deadlock with his eighth league goal of the campaign to join Sergio Aguero at the top of the competition's scoring charts.
Mason Mount and N'Golo Kante were also on target, either side of Danny Ings pulling one back, as Lampard's men netted three first-half goals for the second successive Premier League away trip.
Substitute Michy Batshuayi scored the only goal of a low-key second half to seal the win for Chelsea, which rises to fifth on the table.
Abraham lifted Callum Hudson-Odoi's straight pass over a hesitant Angus Gunn to give Chelsea the lead 17 minutes in, the strike being awarded by goal-line technology despite Maya Yoshida's acrobatic clearance.
The visitors doubled their tally seven minutes later as Mount took Willian's pass in his stride and fired past Gunn, but Southampton was given a lifeline when Ings got in front of Kurt Zouma to divert the ball home.
Chelsea's two-goal lead was restored before half-time, though, as Kante's long-range effort deflected off Jan Bednarek past a wrong-footed Gunn.
Ings rounded Kepa Arrizabalaga but could not find a way past covering Chelsea midfielder Jorginho on the line, while up the other end Gunn kept out Abraham and Hudson-Odoi, who was making his first league start of the season.
But Southampton ultimately offered little in the way of an attacking threat after the interval, with Chelsea instead adding to its tally a minute from time through Batshuayi's composed finish after he had exchanged passes with fellow substitute Christian Pulisic.