The Saints looked set for their sixth victory in seven games when Jan Bednarek hooked in and Shane Long headed home for his baover first of the season.
However, the momentum shifted after the break. Portuguese teenager Pedro Neto, exceptional for Wolves so far this season, reduced the deficit after controlling Adama Traore's delivery from the right.
Jimenez slotted home from the spot to bring the scores level after Jonny had been sandwiched by Jack Stephens and Cedric sagame Soares. Referee Darren England, making his Premier League debut, pointed for a corner before his decision was overturned by VAR.
And with 14 minutes left the fightback was complete when Jimenez stroked in after more good work from Traore.