Postpublished at 64 mins
Chelsea's Eden Hazard pulls it back to Marcos Alonso - who loves a shot - and this one from 20 yards is into the arms of Southampton keeper Fraser Forster - his first save of the game.
Costa heads 50th Premier League goal and then fires in low
Romeu and Bertrand score against former club
Hazard buries from 15 yards, Cahill heads home
Terry makes first league appearance since November
Emlyn Begley
Chelsea's Eden Hazard pulls it back to Marcos Alonso - who loves a shot - and this one from 20 yards is into the arms of Southampton keeper Fraser Forster - his first save of the game.
#bbcfootball
Jasper Shiner: Fraser Forster is without doubt the worst keeper in the Premier League this year.
Harsh?
Oriol Romeu marks his return from a two-game ban by fouling fellow Spaniard Cesc Fabregas. He becomes the first Saints player booked.
#bbcfootball
Nikhil: Hazard, Cahill and Costa in my fantasy team, can't get better than that #FPL
#Jealous
Phil McNulty
BBC Sport chief football writer at Stamford Bridge
Diego Costa's header has given Chelsea the vital breathing space they needed and they look locked on course for a seven-point lead at the top of the Premier League.
Stamford Bridge is in buoyant mood and paying tribute to Chelsea manager Antonio Conte.
Cesc Fabregas (103) is now outright second for most Premier League assists, one ahead of Frank Lampard (102), but still well below Ryan Giggs (162).
Southampton were good enough to perhaps edge the first half so we can't rule them out yet and Dusan Tadic forces a good save down low from Thibaut Courtois.
Manolo Gabbiadini then bicyles a shot wide.
Diego Costa's 50 Premier League goals have come in 85 games - one fewer than Luis Suarez's half-century.
Chelsea striker Diego Costa scores his first Blues goal in eight games and surely they are going seven points top. Eden Hazard feeds Cesc Fabregas who crosses for his fellow Spain international to nod home from six yards out.
That's Costa's 50th Premier League goal.
Diego Costa
Granada 0-1 Malaga
It looks like Tony Adams is heading for his third successive league defeat since becoming manager of relegation-doomed Granada - his side are 1-0 down at home to Malaga with about 25 minutes left to play.
The Spanish club are 18th in La Liga and seven points from safety with only four games remaining after tonight's match.
Southampton break but Cedric Soares latches onto a pass that was meant for Sofiane Boufal and the move is over.
Chelsea midfielder Cesc Fabregas slides in and eliminates Oriol Romeu. Definite booking.
The second half is under way. Arguably a bigger 45 minutes for Spurs than Southampton.
#bbcfootball
Syed Umar: Don't mind the recent lack of clean sheets. So many goals in recent matches we are very entertaining
Aamer Iqbal: Am I in the minority in hoping Chelsea mess up the title run after they downed tools last season? Not a Spurs fan by the way
That was defender Gary Cahill's seventh goal for Chelsea this season in all competitions.
He also scored for England against Scotland back in November.
Only John Terry (40) has scored more goals in the top-flight than Cahill (26) among current Premier League defenders - excluding penalties.
Chelsea 2-1 Southampton
Pat Nevin
Ex-Chelsea winger on BBC Radio 5 live
What a great game of football this is. Very open with two teams attacking all the time. Boufal and Tadic have been superb, the shackles are off at Southampton, they are enjoying themselves.
But Chelsea have a gearbox and they are going through them when they need to.
Phil McNulty
BBC Sport chief football writer at Stamford Bridge
Chelsea made the perfect start but had failed to capitalise - but Gary Cahill's header has calmed growing anxiety around Stamford Bridge.
How Chelsea needed that because Southampton were growing in confidence the longer that first half went on.
Chelsea 2-1 Southampton
That was the last action of the first half, and Chelsea lead at the break.
On the stroke of half-time Chelsea are ahead again. The corner is played in and half-cleared, but it comes back into the box and Marcos Alonso heads it on.
Diego Costa fancies a wonder-goal and throws himself in for a bicycle kick. But just before it reaches him, Gary Cahill gets his head onto the ball and sends it into the back of the net. Narrowly avoided losing his head there.