Matthew Morgan and Ronan O’Gara exchanged penalties as the scores remained level at the break.
Damien Varley crashed over within minutes of the restart but Thomas replied as honours remained even.
The draw saw the Ospreys miss the chance to move into the play-off places but the closed the gap on the Scarlets to a single point, while Munster remain sixth.
Wales second-row Alun Wyn Jones, who could be called into action against Scotland next week, was released to the Swansea-based region.
He came through the 80 minutes unscathed but felt the draw was an opportunity missed.
“It was an attritional game,” said Jones.
“You always expect an attritional half but it was attritional all game. Both teams probably deserved to win and the result isn’t good for either of us.”
O’Gara opened the scoring early on at Thomond Park but Morgan replied and the opposite fly-halves continued to exchange shots at goal in an eventless half.
Munster took a major stride towards victory when Varley burrowed over following a sustained period of pressure early in the second-half and O’Gara converted.
They appeared on course for victory but the Ospreys dug-deep and opportunity arose when Stephen Archer was sent to the sin-bin.
The Ospreys instantly capitalised on their numerical advantage and Thomas crashed over following a succession of strong forward charges.
Morgan maintained his flawless display with the boot and it was enough to secure a share of the spoils as both sides hung on.
