The Saints capitalised on defensive errors to take a 2-0 lead in the first half with goals from Jay Rodriguez and Adam Lallana.
Christian Eriksen sparked the revival on 31 minutes, drilling home from close range after Nathaniel Clyne failed to clear Kyle Naughton’s cross.
The Danish playmaker was there again just 40 seconds into the second half to tap home after great work from Roberto Soldado down the right, the striker outmuscling Dejan Lovren before leaving Christian with the easiest of tasks.
Nacer Chadli was denied by Artur Boruc, Christian shot into the side-netting and Callum Chambers made a last-ditch block to thwart Roberto as we pushed for the winner.
With the clock showing 91.52, Jose Fonte headed Hugo Lloris’ long free-kick out to Christian and he squared for Gylfi Sigurdsson to fire home a dramatic winner from 25 yards.
“I was gutted after 28 minutes and we conceded two poor goals, we know that,” said Tim.
“We needed to dig deep and try to find a way to win the game and I’m so proud of the lads that we managed to achieve that.
“We knew it was going to be tough and to trail 2-0 at home and come back to win 3-2 is a massive achievement.
“Christian gets himself in positions to score goals and possesses real quality. He affects the game, doesn’t just take part in it, even with that pass to Gylfi late on.
“Gylfi gave us a real spark and deserved his goal. It doesn’t just happen, he’s out there (working on) finishing with Les Ferdinand every day. That’s why he scores goals.
“It was a big win for us. We can now concentrate week to week on the Premier League and we’ll try to accumulate as many points as we can.”