It looked as though Munster would come away from the Kingspan Stadium with the spoils of victory as they headed into the closing moments of the match ahead.
But replacement Paul Marshall found his way over the line with the final play of the match to move his side within two and an ice-cool conversion from Paddy Jackson meant it was honours even at the end.
Now Munster must look to next week's clash with Newport Gwent Dragons as they aim to close the regular season on a high and secure home-turf advantage.
"We came up here to get the points, and Ulster always play until the end. But we got two points and are now level on 70 with Ospreys and Glasgow so it's good," said Stander.
"It was a very physical battle up front and we knew that if we put in a few good scrums and line-outs we could get up at them. We got a few in here and there but Ulster are always good up front too.
"Next week is the last game of the year, and it's cup rugby for us as we have to get the points and get that home semi-final. We're going to go out, play the game and that's it."
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