Under caretaker boss Keith Hill, Rochdale reverted back to 4-3-3 for the start of the game but, in a dour first half, the only chance of note fell to home striker Glenn Murray on 31 minutes but he headed wide after strike partner Chris Dagnall had floated a perfect cross to him.
It looked like being another awful day at the office for Rochdale when their former striker Lee McEvilly scored with his first touch having come on as a half-time substitute.
It was a route one goal coming literally seconds after Ingham had denied Murray a headed goal from a corner. The ball was funnelled quickly upfield and McEvilly raced through a huge gap in the centre of the home defence to fire home.
Worse was to come for the home side on 56 minutes when keeper Matt Gilks could only parry a mis-hit McEvilly shot and Wales international striker Chris Llewellyn poked home the rebound.
Rochdale then switched to 4-4-2 with the introduction from the bench of French winger William Mocquet and teenager Joe Thompson.
Undaunted by gifting their opponents the lead they continued to press forward with leading scorer Dagnall twice going close before Murray brought his side back into the game converting a cross from Gary Jones.
Dale drew level on 77 minutes when the Wrexham defence failed to deal with a Thompson cross and veteran midfielder John Doolan produced a powerful header that bounced into the net off the underside of the bar.
In the dying seconds Murray was denied a winning goal when he toe-poked a cross goalwards but Ingham made up for his previous error by producing a stunning save.