Worcestershire let a commanding position slip on the second day on the North Wales coast as Glamorgan just managed to save the follow-on and possibly the match.
At 162 for six, Glamorgan were 147 runs shy of the 311 follow-on and Worcestershire seemed well on course towards a fifth victory in six games to boost their promotion hopes.
But Alex Wharf, who had rescued Nottinghamshire at Colwyn Bay seven years ago, launched a lower-order recovery similar to Worcestershire's on the opening day.
With Mark Wallace, the burly Yorkshireman added 105 in 20 overs and then it seemed a formality Glamorgan would pass the follow-on requirement at 304 for seven.
But when Wharf perished to a top-edged hook off Zaheer Khan and Robert Croft drove Gareth Batty straight to cover, two more runs were still required.
It was left to David Harrison, batting with debutant Kyle Tudge, to get the required runs. At the close, Glamorgan had reached 329 for nine.
Earlier, Daryl Mitchell and Madeem Malik had got Worcestershire up to 460 all out before Zaheer took his tally for the season to 60 wickets by claiming Mark Cosgrove with only the second ball of the hosts' innings.
It was the beginning of a good day's work from Worcestershire, especially as seamers Zaheer (right) and Matt Mason, in particular, seemed to extract more from the benign surface than Glamorgan.
Ryan Watkins and David Hemp looked as if they had seen off the threat of the new ball until Watkins attempted an expansive drive and edged to Ben Smith at first slip off Mason.
That brought to the middle Michael Powell, who came to North Wales on the back of compiling 628 runs in 11 days during July including consecutive double-hundreds.
But any hopes he had of extending his purple patch were erased after only 17 balls and 21 minutes at the crease.
He was bowled through the gate by Zaheer, who continued to hurry the batsmen.
From 80 for three, Glamor-gan rapidly sank to 84 for four seven balls later when Hemp went the same way to Nadeem Malik, this time, Smith took a sharper catch at first slip.
Glamorgan's batsmen seemed to get themselves in, only to perish; that was the case with Hemp and Richard Grant and James Franklin, who both fell to Gareth Batty.
Grant played across the line and then Franklin was bowled having appeared to play down the wrong line.
At the start of the day, Mitchell and Malik frustrated Glamorgan's flagging attack for 72 minutes. As the overs ticked by, so Glamorgan's seam attack seemed to get increasingly disillusioned.
The Mitchell-Malik alliance realised 83, a new Worcestershire record for the tenth wicket against Glamorgan, beating the 58 put on by Jim Cumbes and Paul Pridgeon at Swansea in 1981.
Malik did a good job in getting Mitchell to his maiden Championship century before he fell in Croft's seventh over of the morning.