Darren Bent and Shefki Kuqi missed good chances before David Vaughan set up Dean Ashton to hammer in Crewe's first.
It was 2-0 when Kenny Lunt's defence-splitting pass found Ashton but Ipswich hit back after the break and Richard Naylor pulled one back from a corner.
Bent levelled after Crewe failed to clear Kevin Horlock's cross, and Town could have won when Vaughan cleared Ian Westlake's effort off the line.
Ipswich boss Joe Royle
"Two points lost. I don't know how we were behind at half-time to be honest.
"Television will confirm or not confirm my opinion that both goals were borderline offside and we've missed four or five chances that we would have put away with some appendage to our bodies.
"In the second half it was one-way traffic and our goalkeeper was redundant. It was a great comeback and the second half was a great display of in-your-face
passing football.
"You can see it either way and I won't argue. If you're two goals down on foreign soil and you come back it's a great revival. If you miss enough chances to win three games then it's two points lost, which we did and I don't think even Dario will argue with that."
Crewe: Ince, McCready (Walker 68), Moses, Foster, Bignot, Lunt,
Sorvel, Cochrane, Vaughan, Steve Jones, Ashton.
Subs Not Used: Williams, Bell, Varney, White.
Goals: Ashton 24, 27.
Ipswich: Davis, Wilnis, De Vos, Naylor, Diallo (Richards 45),
Miller, Magilton, Horlock, Westlake, Bent, Kuqi.
Subs Not Used: Counago, Bowditch, Collins, Supple.
Booked: De Vos, Magilton.
Goals: Naylor 55, Bent 59.
Att: 7,236.
Ref: R Olivier (W Midlands).