After being outplayed in the first 45 minutes, Tony Carr's team were lucky to come in only 1-0 down at the interval, but then conceded another goal early in the second half.
The comeback started in the 60th minute, when defender Elliott Ward finished well after good work by Ayo Akinsete, and the Hammers were level 10 minutes later when James Allen fed Phil Lumsden, who fired in from the edge of the box.
There were chances for both sides to snatch the winner late on, with West Ham coming close on two occasions in the last five minutes, but the draw was considered a fair result for both teams.
Said Tony Carr afterwards: "Ipswich are a very good side, top of the league, and to be honest we were chasing the ball in the first half. We still managed to create some chances, though, and I always felt that we could turn it around.
"The two goals we scored were both well-worked and the lads showed a lot of character to react like that after going two down. It could have been a real smash-and-grab if we'd taken our chances late on in the game, but overall I think a draw was the right result."
Team: Jackson, Khan, Lumsden, Ferdinand, Ward, Akinsete (Dean 68), Britton, Carrick, Smith, Eastwood (Ritchie 68), Allen. Subs unused: Metitiri, D.McMahon.
*Coverage of the under-17s' match against Ipswich will appear on this site soon.