Wilson wants Warriors to make home feared
of two in the Pro14 title race – thanks mainly to a try double from Alex Dunbar.
But victory came at a cost as new South African prop signing Oli Kibble was forced off with a potentially serious leg problem.
Glasgow had made a powerful start and only frantic defending stopped them scoring. Having weathered the storm, Ospreys began to look more comfortable.
But Warriors grabbed the initiative with a great piece of sprinting by Dunbar.
The centre pounced on a loose ball on halfway before outpacing his markers to cruise over.
Finn Russell added the extras then banged over an offside penalty from close-in.
Ospreys hit back though and Dan Evans timed his run to perfection to leave the Warriors back markers wrong-footed.
Sam Davies converted but sent a long-range penalty narrowly wide a minute later.
The Swansea men levelled the scores in stoppage-time as Sam Davies found the target.
Exchanges were untidy after the restart with Glasgow winger Rory Hughes spilling the ball just a couple of paces short of the line.
Hughes was then forced off with Leo Sarto coming on.The sub was in the right place in 52 minutes to plunge over after a clever offload by Ruaridh Jackson. Russell’s kick was pinpoint from a tricky angle.
Glasgow made the win secure when Adam Ashe snatched a loose Sam Davies pass and raced home from inside his own half – giving Russell a simple conversion.
Dunbar crashed through to make sure of the bonus point.