Ipswich made the breakthrough in the eighth minute of the contest, with Delap turning a cross from Jack Clarke into the back of the net, and the promoted outfit were causing plenty of issues in forward areas.
Villa's quality ultimately shone through as the first period developed, though, with Morgan Rogers making it 1-1 in the 15th minute after smart work from Ollie Watkins, before the latter headed a cross from Leon Bailey into the back of the net in the 32nd minute to turn the game around.
The away side's goalkeeper Emiliano Martinez was at full stretch to keep out a powerful Kalvin Phillips drive late in the first period, with Unai Emery's team entering the interval ahead, but they also had to survive another golden Delap chance, as the striker was denied when he ought to have scored.
Delap was not disheartened, though, as he made it 2-2 in the 72nd minute after bursting into the Villa box, with the striker expertly picking out the bottom corner to spark jubilant scenes inside the stadium.
Both sides were forcing the issue in the latter stages, but neither could find a third, with the points being shared at the end of an entertaining contest in England's top flight.
Villa remain fifth in the Premier League table but have moved onto 13 points, two points behind leaders Liverpool, while Ipswich have risen into 15th, with Kieran McKenna's side now on four points in England's top flight this term.
IPSWICH VS. VILLA HIGHLIGHTS
Liam Delap goal vs. Aston Villa (8th min, Ipswich 1-0 Aston Villa)
Ipswich make the breakthrough in the eighth minute of the contest, and it is Delap with the goal, as the striker finds the back of the net off a cross from Clarke; Delap's effort was straight at Villa goalkeeper Martinez, but he could not keep it out.
Morgan Rogers goal vs. Ipswich (15th min, Ipswich 1-1 Aston Villa)
Villa level the scores in the 15th minute of the contest, and it is a brilliant finish from Rodgers, who combines with Watkins inside the penalty box before sweeping the ball into the back of the net.
Ollie Watkins goal vs. Ipswich (32nd min, Ipswich 1-2 Aston Villa)
Villa turn the match around in the 32nd minute, as Bailey's wonderful cross from the right is headed into the back of the net by Watkins. Ipswich are made to pay for leaving too much space inside their own box.
Liam Delap goal vs. Aston Villa (72nd min, Ipswich 2-2 Aston Villa)
Ipswich level the scores in the 72nd minute of the match, and it is a second goal for Delap, who shows excellent feet inside the Villa box before firing into the far corner of the net.
MAN OF THE MATCH - LIAM DELAP
Delap will feel that he should have scored a hat trick on Sunday, with the striker having chances to register more than twice, but it was still a very impressive 90 minutes from the forward.
The 21-year-old showed excellent composure with both of his goals, and he was a constant menace to Villa with his pace and power in forward areas.
Delap has now scored three times in England's top flight this term, and he should be looking for double figures considering his quality.
IPSWICH VS. VILLA MATCH STATS
Possession: Ipswich 45%-55% Villa
Shots: Ipswich 13-6 Villa
Shots on target: Ipswich 5-3 Villa
Corners: Ipswich 10-0 Villa
Fouls: Ipswich 10-13 Villa
BEST STATS
WHAT NEXT?
Villa's attention will now switch back to the Champions League, with Emery's side set to welcome Bayern Munich to Villa Park on Wednesday night, before hosting Manchester United in the league next Sunday.
Ipswich, meanwhile, will be aiming to build on the strong result when they continue their Premier League season away to West Ham United on Saturday.