Brennan Johnson scored twice before Omari Hutchinson pulled a goal back in a breathless first half full of chances for both sides.
Luke Woolfenden had an equaliser correctly chalked off for offside on the hour mark, then substitute James Maddison's silky footwork set up Djed Spence for Spurs' killer third on 77 minutes.
Dejan Kulusevski curled in the visitors' fourth when Ipswich players were left calling for the play to be stopped for a Jacob Greaves head injury.
Wolves' 1-0 win at Bournemouth means that Town are now five points adrift of safety with 12 games to go.
Blues boss Kieran McKenna made four changes to the side that started the previous weekend's 1-1 draw at Aston Villa.
Axel Tuanzebe, serving a one-game ban for his controversial two-booking dismissal at Villa Park, was replaced by Ben Godfrey at right-back. It was the two-cap England international's second league start since he joined on loan from Atalanta.
The fit-again Leif Davis replaced Conor Townsend at left-back, while Jaden Philogene and Jack Clarke came in for Ben Johnson and the injured Julio Enciso in attack.
Sam Morsy, available again after an abdominal injury, had to make do with a place on the bench as McKenna stuck with the midfield pairing of Kalvin Phillips and Jens Cajuste. Dara O'Shea, once again, wore the captain's armband.
Tottenham boss Ange Postecoglu made three changes to the side that started a 1-0 home win against Manchester United the previous weekend.
The fit-again Daniel Udogie replaced Pedro Porro, with Djed Spence moving from left-back to his more natural right-back role. Archie Gray came in for Ben Davies at the heart of defence, while Brennan Johnson, another back from injury, replaced James Maddison. That meant that Dejan Kulusevski played in a slightly deeper attacking role.
Town burst out the traps and created two good chances inside the opening two minutes of the game.
Jens Cajuste's driving run and pass set Delap away down the right side of Tottenham's box with just seconds played and his well-struck shot stung the palms of Guglielmo Vicario. Jaden Philogene's follow-up shot struck team-mate Omari Hutchinson on the line and, after a frantic spell of play, the offside flag was raised.
Not long afterwards, with Portman Road a cauldron of noise, Davis' sharp throw up the line set Delap away down the side of the box again. This time his low shot went across the face of goal.
The breathless start continued when Son Heung-min set overlapping left-back Destiny Udogie racing away. Dara O'Shea recovered well to show good strength though and Alex Palmer saved bravely at feet.
Delap went even closer in the sixth minute. After Hutchinson won a foul, Phillips whipped in a wide dead ball and Delap's glancing/looping header came back off the angle of bar and post.
Tottenham were the next team to create a good chance. With 13 minutes on the clock, Son blazed past Ben Godfrey and cut the ball back. Lucas Bergvall's shot was blocked by O'Shea and Jacob Greaves did superbly to fling himself in the way of Johnson's follow-up chance.
Ipswich, unfortunately, didn't heed the warning shot. In the 18th minute, centre-back Archie Gray intercepted a pass, played a long ball over the top and Son, after getting in behind Godfrey, drilled in a low cross that Johnson stabbed in from close range.
Town responded well. A thunderous Delap shot from outside the box deflected wide and, from the resultant half-cleared corner, Philogene went close with a swerving long-rang effort. Moments later, after good interplay involving Cajuste, Clarke and Davis, Delap's spin and shot from the edge of the box tested Vicario down low.
It was Tottenham who struck the next blow, however. And it was a carbon copy of their opener as Son once again got in behind Godfrey to cut the ball back for Johnson to side-foot home. Town's marking, in all phases of the move, was slack.
Two minutes later, Son drifted into the same position and, this time, Palmer had to make a smart near post stop. There were groans of frustration around the ground and an inquest among the Town players.
The slugfest continued and Ipswich, having been on the ropes, were able to get the next goal. In the 36th minute, a long kick up field by Palmer led to Phillips sliding a well-weighted pass and Clarke cutting the ball back for Hutchinson to sweep home a fine first-time finish from near the penalty spot.
There was still time, in an action-packed half of football, for Palmer to make a smart stop from Rodrigo Bentancur after he'd intercepted a poor Davis throw and driven forwards to shoot.
McKenna hooked Godfrey at the break, replacing him with Luke Woolfenden and shifting O'Shea across to right-back.
Then, six minutes into the second half, Cajuste twisted awkwardly in a challenge and limped off. He was replaced by Jack Taylor.
There was a subsequent spell where Ipswich were pushing for an equaliser. The Blues thought they had it on the hour mark when Woolfenden stopped to head in Hutchinson's high cross to the far post, but the offside flag had, correctly been raised.
Ex-Norwich man James Maddison was introduced off the bench to resounding boos, but it his quick footwork that led to Tottenham scoring a killer third in the 77th minute. After dancing his way through three Ipswich players he teed up Spence and the full-back's shot inside the box deflected in off Woolfenden.
To rub salt in the wounds, Phillips then became the second Ipswich midfielder of the day to be forced off injured.
The home crowd increasingly felt they weren't getting any decisions off referee Tim Robinson, the man at the centre of that gut-wrenching 1-1 home draw with Leicester last November. That feeling intensified following Tottenham's fourth goal of the afternoon.
When ex-Town loanee Dane Scarlett flicked the ball on he clashed heads with Jacob Greaves and the pair went down. Robinson did not stop the play though and Kulusevski raced away before cutting inside and curling a shot beyond Palmer.
McKenna's men go to struggling Manchester United on Wednesday night.
Ipswich Town (4-2-3-1): Palmer; Godfrey (Woolfenden 46), O'Shea (cpt), Greaves, Davis; Phillips (Morsy 80), Cajuste (Taylor 62); Philogene, Hutchinson, Clarke (Broadhead 68); Delap (Hirst 80).
Unused subs: Muric, Johnson, Woolfenden, Townsend, Szmodics.
Tottenham Hotspur (4-3-3): Vicario; Spence, Danso, Gray, Udogie (Porro 64); Bergvall, Bentancur; Kulusevski; Johnson (Maddison 64), Tel (Scarlett 74), Son (Odobert 74).
Unused subs: Kinsky, Reguilon, Bissouma, Sarr,, Moore.
Referee: Tim Robinson