Suljovic had to come from behind though with 'The Gentle' 2-1 down at one point but he dug deep to claim the tie and set up a clash with either Peter Wright or James Wilson.
It was six 180s and 55% on the doubles for the former Champions League winner who has said that he believes he can win the tournament now.
It was a promising start for Suljovic with him storming to the first set in consecutive legs and hitting a 100 average. Price though wasn't going to come this far in the tournament to hand the tie to Mensur.
In the following set despite squandering three set darts when 2-1 up and having Suljovic missing the bull for the set, Price levelled the tie up at 1-1.
From there the impetus was on the Welshman who went on to hit a 61 finish followed by a 116 checkout with him then going on to wrap up the set 3-1.
In the next set though it was the turning point of the tie with The Gentle sealing the fourth set to force the decider with six 180's and 53% on the doubles at that point.
It looked like Price was going to claim the match though at the beginning of the decider with him smashing in a 130 checkout to go ahead. Suljovic came back to claim a lucky D16 and then D8 due to missed darts which handed the Austrian the match.
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World Grand Prix.
Mensur Suljovic (91.19) 3-2 (84.41) Gerwyn Price
Peter Wright v James Wilson
Daryl Gurney v Gary Anderson
Michael van Gerwen v Dave Chisnall
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