After turning around 5-3 down at the break they stormed back with Callum Black rumbled over to celebrate his 100th appearance and Paddy Jackson banging over the conversion and adding a penalty.
Ulster were caught cold from Glasgow’s first visit to the Ulster red zone in the 10th minute when Lee Jones touching down.
In the 23rd minute Ulster’s Pienaar knocked over a penalty. Everything appeared to change in the 52nd minute with the sprightly Gilroy carving through the Glasgow defence and setting up the platform for Black to crash over. Jackson, who came on as a second-half replacement, converted and then added a penalty in the 66th minute.
Ulster had a bag of opportunities to add to their total but Glasgow had the last say when replacement Taqele Naiyaravoro went over in the corner.
S Olding; C Gilroy, D Cave, S McCloskey, J Stockdale (Arnold, 74); S Windsor (Jackson, 40), R Pienaar (Marshall, 30); C Black (McCall, 57), R Herring (capt) (Andrew, 43), R Lutton (Ross, 77); A O’Connor, F van der Merwe, R Diack, S Reidy (Henry, 52), N Williams (Wilson, 64).
P Murchie; L Jones (Naiyaravoro, 64), G Bryce, S Johnson, R Hughes; G Hunter (Horne, 54), A Price (Hart, 64); R Grant (Allen, 59), P MacArthur (Malcolm, 36), S Puafisi (Rae, 69): G Peterson, L Nakarawa (Strauss, 59): R Harley, S Favaro (Fusaro, 40), R Wilson (capt).
Marius Mitrea (Italy)
Black try; Jackson penalty, con; Pienaar pen;
L Jones, Naiyaravoro tries)