Ole Gunnar Solskjaer’s side found themselves 2-0 down at the break at St Mary’s following goals from James Ward-Prowse and Jan Bednarek.
Cavani was introduced at half-time in place of Mason Greenwood and the 33-year-old started the comeback when he set-up Bruno Fernandes to halve the deficit.
The former Paris Saint-Germain forward then got himself on the end of a Fernandes shot to equalise, before scoring a late diving header to seal the three points for United.
Cavani has only made one start for United since his arrival as a free agent but his work ethic and dedication has resonated well with his new team-mates, who have been impressed by the veteran’s professionalism.
That was evident as Pogba – who missed today’s game with an ankle injury -took to Instagram shortly after the final whistle to hail Cavani.
The Frenchman shouted ‘El Matador’ twice during the video, referring to Cavani’s nickname.
Pogba tagged Cavani in the post and followed it with two ‘flame’ emojis to further express his happiness at the win.
However, Solskjaer confirmed before kick-off on the south coast that Pogba could resume full training on Monday and he hopes to have him fit for the visit of PSG on Wednesday.
‘It is improving and hopefully he will be training on grass today or tomorrow,’ said Solskjaer of the midfielder.
‘Hopefully ready for Wednesday.’