After a tight first half Glebe had too much for a spirited Tower Hamlets and claimed all three points.
In the opening exchanges Jamie Philpot caused problems with a cross that Tayo David could only punch out but it didn’t fall kindly for Lanre Azeez, and he was unable to finish. Philpot was again in action soon after when a corner was half cleared and he shot first time but David made the save.
At the other end, Hasan Yilmaz cut in and hit a good shot that George Kamurasi did well to turn around the post, then Mustafa Said let fly with a shot that flew wide.
Bradley Wilson created another opportunity for Glebe but Dami Olorunnisomo, arriving late, screwed wide.
On twenty minutes Glebe went ahead when Charlie Penny got on the end of Philpots low diagonal cross to finish from close range.
Five minutes later parity was restored. Necati Gench sent a long ball through and Sezgin Aleksiev lobbed the out-rushing Kamurasi, and into the empty net. He came close again shortly afterwards but Kamurasi got down well to save.
Chances were few and far between for the rest of the first half as the teams cancelled each other out although Philpot had a couple of shots late on, the first of which was touched round the post, and the second went wide of the near post.
Early in the second period Philpot burst through but David made the save. However, the game remained tight until just after the hour mark when Glebe went back ahead. A corner found Penny in space and he finished superbly.
The hosts came close to levelling again when Gench blasted a free kick towards the top corner but Kamurasi made a brilliant save to tip it over.
Penny was offered a chance of going for his hat-trick when David picked up the ball outside the penalty area from a drop ball but the Hamlets’ goalkeeper redeemed himself by tipping it over. Penny then beat the offside trap but David forced him wide and he could not slide it home.
Glebe added a third in the final minute when Philpot pulled it back and Wilson slotted it into the bottom corner.
As a result Tower Hamlets remain three points adrift of safety while Glebe closed the gap between them and the top two.
Tower Hamlets: David, Gorges, Bingol, Ariogiu, Prushi (Sahaouin 67), Magbu, Gench, Said, Aleksiev (Zeddini 57), Denby, Yilmaz.
Subs not used: Fiauian, Mario.
Goalscorers: Aleksiev (26)
Yellow cards: Koca (Manager) Prushi, Ariogiu
Glebe: Kamurasi, Olorunnisomo, Parsons, Johnson, Morath-Gibbs, Holder, Penny, Everett (Hever 66), Philpot, Wilson (Graham 90+), Azeez (Chin 63).
Subs not used: King-Elliott, Baugh.
Goalscorers: Penny (20), (62), Wilson (90)
Yellow cards: Everett
Referee: William Donnelly
Assistants: Kieran Parrott and Alexis Stacchini