The visitors took the lead in the first fifteen minutes after capitalising on some lacklustre defending from Town. Sara Degooyer found herself unmarked in the six-yard box and swept home a low cross from the right-hand side.
It could have been two in quick succession for the Londoners but Eliza Diaz's speculative dipping volley smashed the crossbar.
However the away side did double their advantage with a scintillating counter-attack. Molly Peters, who had terrorised Town with her electric pace, broke through the middle of the field before racing past four Ipswich defenders, rounding Sian Fagg and slotting into an open net.
Town's horrific first-half would continue as Peters added to her tally on the stroke of half-time, this time converting from close range after more sloppy defending from Ipswich.
To their credit, Town responded well after the break and were awarded a penalty moments after the restart as Natasha Thomas was hauled down in the area. Crump stepped up and held her nerve to dispatch the spot-kick low to the keeper's left to give Town a lifeline.
Crump was again at the heart of the action as the Tractor Girls netted a second goal just two minutes later, with her corner somehow beating Enfield keeper Grace Brooks and sneaking it's way in at the near-post.
The goals provided a much needed spark for Ipswich as they started to carve out more chances, with Zoe Cossey next to go agonisingly close to levelling for Town.
Enfield then had a glorious chance to confirm the three points on the break but Peters was thwarted excellently by the alert Town stopper Fagg. Natalie Richardson was then cursing her luck as she squandered a great opportunity to level late on as she blasted over the bar unchallenged.
The dramatic ending would soon escalate as a massive scuffle broke out after a late tackle on Town defender Laken Duchar-Clark, which resulted in Enfield substitute Tia Bailey being shown a straight red card for a headlock on Ipswich midfielder Mollie DeBell.
It took staff and officials almost five minutes to eventually calm down the brawl before play was restarted.
Ipswich continued to press for a late equaliser with Sophie Welton unlucky to see her effort miraculously cleared off the line.
Finally, after seventeen minutes of added time, Town finally found a leveller and claimed a well fought point as Crump's dangerous corner was bundled over the line by Enfield defender Claire Ford.
Town XI: Fagg (GK), Ball (Arnoup), Duchar-Clark, Cooper, Pannifer, Welton, Crump (c), Craddock (DeBell), Cossey (Turbill), Richardson, Thomas.