The point ensures the Hampshire club climb off the foot of the table although they remain in the relegation zone, now just two points from safety.
The visitors created the better opportunities in a forgettable first half at Spotland. The opening half-hour was devoid of openings at either end, but the Shots closed the first period positively.
Danny Rose saw a measured volley from the edge of the area palmed away by Josh Lillis while Craig Reid had a goalbound effort blocked by Phil Edwards.
Rose delivered a well-worked free-kick for Asa Hall at the back post and his header beat Lillis but was hacked off the line by George Donnelly as Rochdale limped towards the interval fortunate to keep their clean sheet intact.
Keith Hill's side responded after the break and edged ahead in the 52nd minute. Michael Rose and Joe Thompson teamed up on the right to release striker Donnelly and he slipped an angled finish past goalkeeper Jamie Young.
The visitors, however, were on level terms in the 72nd minute when Ben Herd's free-kick was spilled by Lillis and substitute Mekki pounced on the loose ball to score.
And the Shots came close to snatching victory when Hall smashed a side-footed effort against the woodwork, while at the other end Bobby Grant fired over the top when one-on-one against Young.