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, who rise up to fifth in 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 were 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 their tally a minute from time through Batshuayi's composed finish after he had exchanged passes with fellow substitute Christian Pulisic.
What does it mean? Lampard's Chelsea building momentum
Chelsea started the season slowly but they head into the October international break on the back of a four-game winning streak in all competitions.
Successive victories in the Premier League sees them move level with fourth-placed Leicester City and they do not face a side currently above them until travelling to Manchester City in late November.
Abraham maintains impressive form
In the week he was called up by England, Abraham scored his ninth goal of the season in all competitions - the joint-most of any Premier League player, alongside Raheem Sterling.
Southampton's defending was poor - and the less said about Gunn's part in the first two Chelsea goals the better - but Abraham deserves credit for continuing to take his chances when they fall to him.
Chelsea's defence still fragile
Southampton got in behind Chelsea on a number of occasions in the first half, most notably for Ings' goal after four visiting players failed to stop the run of Yan Valery.
In the 69 games that Lampard has managed between Derby County and Chelsea in all competitions, his teams have only kept a clean sheet 15 times.
Key Opta facts
- Southampton have lost three consecutive Premier League games for the first time since October 2018, when Mark Hughes was in charge.
- Chelsea have won each of their last four games in all competitions, equalling the longest win streak of Frank Lampard's managerial career to date (also four games - August-September 2018 with Derby).
- Southampton have won just one point in Premier League home games this season (P4 W0 D1 L3); the fewest in their opening four home fixtures of a top-flight campaign since 2001-02 (also one point).
- No player in the top four tiers of English football has scored more league goals than Tammy Abraham in 2019 (20 - level with Sergio Aguero, Teemu Pukki and James Collins).
- Mason Mount has scored three goals in four away appearances in the Premier League this season, as many as he managed in 20 away league games at Derby.