The Minstermen went close in the opening minute when Olly Dyson’s long-range shot was pushed over the crossbar by Dale keeper Louie Moulden.
Callum Harriott cut in from the right to fire across goal as the visitors finished the half strongly.
Rochdale forward Iain Henderson sent a looping headed wide just after the hour and then saw a late goal ruled out for offside before York keeper George Sykes-Kenworthy made a fine save from Tyrese Sinclair’s volley to help earn his side a point.
Moors came close in the first half when Jamey Osborne had a chance from 25 yards but it was easily caught by visiting goalkeeper Rory Watson before Joe Newton’s effort flew just wide of the post.
They continued to threaten after the break when Newton’s dangerous cross was cleared before Watson was forced into another save.
Jack Stevens eventually found the breakthrough for Solihull in the 87th minute, smashing the ball into the top corner from Callum Maycock’s cross, meaning they finished fifth in the play-off spots.
York, who had lost their first two games, were ahead after 10 minutes when Dipo Akinyemi volleyed home his second goal of the season.
Chris Conn-Clarke’s cool finish levelled matters after 37 minutes, but York instantly regained the lead through Callum Harriott’s first goal for the club.
Altrincham preserved their unbeaten record when substitute Matty Kosylo scored with his first touch midway through the second half.
