Having topped the table going into the penultimate weekend of the regular season, Glasgow had dropped to fourth after a damaging capitulation against the Lions in South Africa last time out.
Leinster’s 33-7 win over Connacht means the Irish side lead Glasgow on points difference, meaning Glasgow must now hope Munster fail to beat Ulster while Bulls also fall short against Sharks to secure a top-two finish.
But this was really about Warriors rediscovering their mojo before next weekend’s home quarter-final and they took barely three minutes to get up and running, Bhatti touching down to finish off a rolling line-out maul.
A scrappy 20 minutes ensued and it was Zebre, with only one win to their name all season, who had the better of the territory and possession and a brace of penalties from Montemauri bought the Italians back within a point.
Three times Glasgow thought they had scored their second try only to be denied. Cancelliere spilled a bouncing ball over the tryline, a Rowe try was ruled out by the TMO for crossing in the build-up and Sione Tuipulotu was held up over the line.
Finally, Warriors went over again when Matthews took up his trademark position at the back of the maul to dot down for his 13th URC try this season.
A monster penalty from full-back Trulla from inside his own half reduced the arrears and the full-back was instrumental as the visitors struck in the final play of the first-half to leave Scotstoun stunned.
Some brilliant footwork from Trulla opened up the Glasgow defence and the ball was eventually fed to Miontemauri to dive over in the corner. The fly-half converted his own try wonderfully from the touchline and sent his side in 16-12 up at the break.
Warriors were toiling until Tuipulotu seized on a loose ball, bounced off a defender and sent Rowe in under the posts for a try that drew a huge sigh of relief from the home support.
That relief lasted no time at all as a pass from Rory Darge in his own 22 was picked off by opposite number Bravin, who ran in untouched to wrestle the lead back for Zebre.
Glasgow finally strung some phases together and, when the ball was spun out to Cancelliere, the Argentine kept his cool to go over for the bonus-point try.
George Horne’s conversion edged the home side in front by a point, but Montemauri struck again from the tee and Warriors were staring down the barrel of a shock defeat.
It was time to revert to the tried and tested as Matthews rumbled over at the back of the rolling maul once again to touch down for his second try.
Substitute Jordan crossed in the final play to add some gloss to the scoreline, but Warriors got away with one here.
No matter their opponents in next week’s quarter-final, a repeat performance will surely bring their URC challenge to an abrupt end.
