The forward celebrated his 22nd birthday on Wednesday and marked it with his first goal in the Champions League away to Lille and the next day he was called up by England again.
Abraham's exceptional form continued at St Mary's with the number nine opening the scoring before Mason Mount – also in Gareth Southgate's latest squad – and N'Golo Kante added further first-half strikes.
Southampton showed great intent from the first whistle with Nathan Redmond firing over inside 60 seconds before the hosts won two corners in quick succession.
Jorginho received a booking in the 12th minute for a foul on Shane Long, but the Blues soon got rid of their rustiness and began to dictate play.
Five minutes after that yellow card, they put the Saints under pressure and made the most of some terrible defending to take the lead.
Callum Hudson-Odoi produced a wonderful pass over the top and Abraham beat Angus Gunn to the ball, flicked over the Southampton goalkeeper and grabbed his ninth of the season by the finest of margins – with Maya Yoshida attempting to clear. However, referee Paul Tierney got the alert on his watch that the whole ball was over the line.
It was 2-0 in the 24th minute. Gunn's rushed clearance saw the ball eventually come for Willian, who exchanged passes with Jorginho before the Brazilian found Mount in the area, who curled in for his fourth of the term.
At this point Frank Lampard's team looked set to run riot – but questionable defending by the visitors gave this open encounter a third goal by the half-hour mark.
Yan Valery – recalled to the starting XI – dribbled past Fikayo Tomori too easily on the right and his cross was side-footed beyond Kepa Arrizabalaga by Ings, despite Kurt Zouma sliding in on the forward.
Hasenhuttl would have wanted this to be a turning point, but more slack play at the back saw them concede a third in the 40th minute.
Marcos Alonso picked out Kante and the Frenchman was given plenty of space and saw his 20-yard effort take a deflection off Pierre-Emile Hojbjerg and leave Gunn with no chance.
Southampton almost pulled one back in first-half stoppage time, when Tomori gave the ball away again, this time to Ings in a dangerous position, but his effort – which had beaten Kepa -was wonderfully prevented from finding the net by Jorginho.
The message from both managers at the break had clearly been to tighten up at the back, with chances at a premium for 20 minutes after the interval.
James Ward-Prowse curled over from a free kick in a dangerous position, then Abraham's low effort was comfortable for Gunn.
The Blues went through the gears again, though, but Hudson-Odoi and Willian saw efforts blocked before several substitutions were made.
Lampard handed Christian Pulisic his first league minutes since August 31 with 10 left and he responded with a smart assist for fellow sub Batshuayi, who drilled through Gunn's legs in the 89th minute as Chelsea comfortably secured a fourth straight win.