The Saints went ahead early thanks to a goal from striker Jay Rodriguez, but two debut goals Ba began the comeback, with Victor Moses, Branislav Ivanovic and Frank Lampard putting the Blues one step closer to defending their title.
Tom Cleverley gave the visitors the lead when he sidefooted in before James Collins headed the equaliser, his first goal since returning to the club. Collins gave the Hammers the lead with another header after the break.
But with seconds remaining, Van Persie latched on to Ryan Giggs’s through-ball to earn the visitors a replay.
Aston Villa also came back from 1-0 down as they beat Ipswich Town 2-1 to give manager Paul Lambert some brief respite.
Michael Chopra had given the Tractor Boys the lead but a returning Darren Bent, against his old club, and Andreas Weimann scored in the second half as the Villans stole a late victory.
Manchester City easily dispatched Championship promotion hopefuls Watford with a 3-0 win, courtesy of goals from Carlos Tevez, Gareth Barry and 17-year-old forward Marcos Lopes.
Tottenham v Coventry had been earmarked as a possible shock as many reminisced about the Sky Blues’ 1987 FA Cup final win. But Andre Villas-boas put out a strong side and Clint Dempsey’s double, which sandwiched a Gareth Bale strike as Spurs eased to a 3-0 win.
Sunderland staged a magnificent comeback to draw 2-2 with Championship side Bolton.
Chung-Yong Lee and Marvin Sordell’s goals either side of the break put Wanderers in a seemingly comfortable lead, but late goals from Connor Wickham and Craig Gardner meant that the Black Cats can take the tie back to the Stadium of Light for the replay.
Wigan were given an FA Cup lifeline when a Jordi Gomez penalty earned his side a reply at the DW Stadium after a 1-1 draw with Bournemouth. Eunan O’Kane’s long-range drive put The Cherries in front but their hopes of progressing to the next round were dashed when Gomez scored the equaliser with 20 minutes left to play.
Reading were another side who went a goal down before coming back to win as they beat Crawley Town 3-1. Nicky Adams had put the League One side ahead but Adam Le Fondre (2) and Noel Hunt sent the Royals into the fourth round of the competition.
There was late drama at Loftus Road as Keiron Dyer’s late, late strike got Harry Redknapp’s QPR side a 1-1 draw with West Brom who had led through Shane Long. The two teams will now play out a replay.
As will Fulham and Blackpool as goals from Ludovic Sylvestre and Girogos Karagounis saw the match end 1-1.
Crystal Palace and Stoke City will face each other again in a third round replay at the Britannia Stadium after playing out a goalless draw in which Palace looked the more impressive side.
And elsewhere there were two big lower league shocks as Macclesfield Town beat Championship leaders Cardiff City 2-1 and Blue Square Premier side Luton Town beat Wolves 1-0.