Ipswich's Wes Burns opened the scoring early in the second half, but the visitors' lead lasted just 10 minutes, with Southampton, fresh from their FA Cup semi-final defeat by Manchester City, equalising through Ryan Manning's free-kick from the edge of the box.
And home fans at St Mary's had even more to celebrate when Cyle Larin put the Saints ahead with 10 minutes of normal time remaining.
But Ipswich were back level in the 87th minute when, following a corner, substitute Jack Clarke drilled a left-footed shot from the edge of the area past Saints goalkeeper Daniel Peretz into the bottom left corner.
Clarke, Ipswich's leading scorer this season, almost sealed victory two minutes later when his shot hit the base of the post, ricocheted past Peretz and then rolled past the post for a corner.
And in the third of five minutes of added-on time, Ipswich put the ball into the net again, only for the effort to be rightly ruled out for offside before Peretz denied Clarke with a superb save.
Only the top two at the end of the regular season are guaranteed places in English football's lucrative top-flight, with leaders Coventry already assured of the Championship title.
Had Ipswich - like Southampton, relegated from the Premier League last season - won, they would have been three points clear of Millwall and all but guaranteed promotion, such is their vastly superior goal difference.
But the draw means they must win at home to Queens Park Rangers on Saturday to assure themselves of second place, with Ipswich now a point ahead of Millwall and two clear of fourth-placed Middlesbrough, both of whom could finish runners-up to Coventry.
The draw ended Southampton's hopes of automatic promotion. But the Saints will be involved in the play-offs, featuring the teams finishing third to sixth, which will determine which other team enters the Premier League.
Following a lacklustre first half, Ipswich went ahead in the 48th minute when Burns powered a shot to Peretz's left and into the top corner, via a slight touch off the keeper's fingers.
But Southampton hit back 10 minutes later after Jacob Greaves was yellow-carded for a fierce challenge on Finn Azaz just a yard outside Ipswich's penalty area.
Ryan Manning's powerful free-kick just flicked off Marcelino Nunez, but the deflection was sufficient to take the ball to the left of Christian Walton as the Ipswich goalkeeper dived to his right.