Rochdale managed a draw against Doncaster Rovers at home, with the final score 1 - 1 on Saturday.
Aaron Morley's 66th-minute strike looked set to hand Rochdale a second successive victory to start the League One season, before Kieran Sadlier struck two minutes into added time, with a header.
During an evenly-contested first half, Dale hit the woodwork when Morley's lofted pass was flicked on by Callum Camps towards the run of Rekeil Pyke, but the on-loan striker's effort thudded against the foot of the post.
Lawlor also made saves to deny Morley and Pyke.
The visitors came close when James Coppinger's corner was met by Matty Blair, whose header was parried by Dale keeper Robert Sanchez against the back of a team-mate, the ball flying narrowly wide of the upright.
Dale took the lead in the 66th minute when a corner was headed out to Morley on the left and he curled a teasing delivery towards goal which bamboozled Lawlor. By the time the goalkeeper had reacted, the ball was past him and in the net.
But, two minutes into time added on, Sadlier rose above the Dale defence to meet Jon Taylor's corner and head past Sanchez.
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