Town enjoyed the better of the early chances with first Paige Wakefield nearly catching Charlotte Ferguson off her line with a first-time distant effort but the scrambling Wimbledon goalkeeper did well to tip over the bar.
Then from the resulting corner, Toni-Anne Wayne collected the short-ball before curling just wide of the far-post.
Soon after, the Blues had the ball in the net as Lindsey Cooper flicked Amy Nash’s free-kick into the net but the linesman’s flag was up on the far side.
Town may have had the better of the chances but Wimbledon were still threatening, forcing Sian Fagg into a couple of reactionary interventions to avert the danger.
Town could have gone in front on the stroke of half-time but substitute Zoe Cossey’s cross to the back-post was just too heavy for the arriving Nash.
Ipswich nearly got off to a perfect start to the second-half as Cossey cut in and forced a parried save from Ferguson but Amanda Crump’s subsequent follow-up dropped onto the roof of the net.
However, the Tractor Girls would soon be punished for not taking their chances as the Dons took the lead.
After springing a rapid counter-attack, Heasman found herself in behind the Town backline before finding the back of the net with a sweet strike.
Ten minutes later and things went from bad to worse as Wimbledon doubled their advantage following a mistake from a Town set-piece.
Wayne’s underweighted free-kick on the halfway line was intercepted by Manzi, who raced through on goal and punished the blues by firing into the far corner.
Ipswich looked to manufacture a response with the introduction of the lively Georgia Box but were unable to carve out any clearcut chances.
In the closing stages of the game the Dons simply dug in and held on to ensure the three points returned to southwest London.
Town XI: Fagg (c), Ball, Petley, Cooper, Pannifer, Wakefield (Cossey), Flatt, Crump, Nash, Thomas, Wayne (Box)
Unused: Clarke (GK), Moore