At stumps on the rain-marred day, Glamorgan reached 133 for three, with Zaheer claiming two wicket.
Inserted after a delayed start, Australian southpaw Mark Cosgrove slammed 61 from 91 balls and put up a 102-run partnership with Dan Cherry (33) to frustrate the home side, who had opted to bowl first.
Zaheer, who was erratic in his opening spell, finally induced cosgrove to edge a delivery and Steve Davies gleefully accepted the catch behind the stumps.
The batsman hit Nadeem Malik over long-off for a six besides 11 fours.
Zaheer was later warned for running on the wicket but he soon mended his way and came back to remove Michael Powell (4), another caught behind dismissal.
Zaheer's bowling figure, so far, read 16-8-41-2.
In another Division Two match, Dinesh Mongia will lead Leicestershire in the absence of regular captain Jeremy Snape, who is nursing a cracked thumb which he sustained in the match against Derbyshire last week.
''...Dinesh Mongia will skipper the Leicestershire side in the absence of Snape and vice-captain Darren Robinson, Aftab Habib and youngster Steven Clarke have been drafted into the 12-man squad, the club said in its website.