Town had been on course to record a fourth straight win and close further ground on the top six after Grant Leadbitter struck from distance inside the opening 10 minutes.
But they capitulated either side of the break as Tony Mowbray's side overturned the lead thanks to Andy Halliday's tap-in and Scott McDonald's close-range finish before half-time, with Andrew Taylor adding a third soon after the break.
Connor Wickham, who had two efforts ruled out for offside, finally netted when he headed home from six yards to give Ipswich hope and they made sure of the point when Leadbitter scored his second from the penalty spot.
Despite the rally, their season looks over as they sit eight points off the play-offs with five games to play.
Mowbray, meanwhile, was left to celebrate a sweet return to Portman Road, where he spent five years as a player, as his side secured a second away win in three days to make absolutely sure of safety.
Paul Jewell's men knew they had to put in a near-perfect record between now and the end of the season if they were to sneak into the play-offs and their fast start reflected that.
After early pressure, they forced a corner and Leadbitter gave his side a sixth-minute lead when he drove home his fourth league goal of the season, which took a healthy deflection.
Ipswich remained dominant in terms of possession and territory and they thought they had a second after Smith parried David Norris' header into the path of Wickham, but the Football League Young Player of the Year was flagged offside after hitting the rebound home.
But then, after barely creating anything throughout the opening 40 minutes, Boro turned the game on its head by scoring two goals inside 90 seconds to take an unlikely lead.
First Halliday was left with the simplest of finishes in the 42nd minute after Damien Delaney's sliced clearance left Town keeper Arran Lee-Barrett stranded and bounced off the bar and into the substitute's path.
And before the Boro supporters could catch their breath they were celebrating again when Halliday turned provider with a cute touch which found McDonald free inside the six-yard box and the former Celtic midfielder made no mistake to net his fifth of the season.
Boro did not have to wait long for their third as they struck again in the 51st minute and Halliday was again the architect as he slid in Taylor and he collected the ball and finished in style pass Arran-Barrett.
Ipswich had to respond quickly and they had the ball in the net minutes later, but Wickham was again in a offside position and it was ruled out.
But he finally beat Boro's offside trap in the 64th minute to give his side hope of earning at least a point when he met Jimmy Bullard's delivery with a thumping header.
Wickham went close again, but was denied by Smith, before Town completed the comeback after Leadbitter converted a penalty with 14 minutes remaining when Matthew Bates had fouled Lee Martin.
And Ipswich wasted two opportunities to take all three points as Smith was called into action to produce two brilliant saves, first to deny Wickham and then Delaney as it ended all square.