Day seven of the £450,000 event saw the first two quarter-finals take place at the Aldersley Leisure Village, with the winners advancing to Sunday’s final day of the tournament.
International Darts Open champion Price reached the semi-finals for the first time, defeating Simon Whitlock 16-15 in a thrilling replay of their Group F encounter.
European Championship runner-up Whitlock, who was starring in his third Grand Slam quarter-final, landed a magnificent 146 checkout in the opening leg as he raced into a 7-3 lead.
The Australian fired in 12 180s in the match, but a resilient Price fought his way back into the contest and levelled it up at 10-10 to set up a tense finale.
With nothing to separate the pair at 13-13, Whitlock landed three maximums in two legs to go within one of the matches at 15-13, only for Welshman Price to roar back after Whitlock missed four match darts across two legs.
Price missed the bullseye for a 164 finish and then survived a fifth match dart before pinning double 12 at the first attempt to lead for the first and only time and book his place in the final four.
Price will now take on Suljovic, who also reached the semi-finals for the first time as he proved too strong for Wednesday’s nine-dart hero Dimitri Van den Bergh, running out a convincing 16-9 winner.
The repeat of May’s German Darts Masters final saw Suljovic lead throughout the contest, never allowing the young Belgian a way in.
Suljovic landed a 167 checkout to go 2-0 up and soon found himself in a commanding 8-3 lead before Van den Bergh battled his way back to 12-8.
However, that was as close as the World Youth Champion got to restoring parity as Suljovic won four of the last five legs to romp into the final four.
“I was worried I was going to go out in the group stage so it’s amazing to reach the semi-finals,” said Suljovic.
“I had to be at my best against Dimitri, he is a brilliant player and as always I have to thank the crowd for supporting me – they were great.”
The knockout stage continues on Saturday with the last two quarter-finals taking place, as reigning champion Michael van Gerwen takes on Jonny Clayton and Gary Anderson faces German BDO qualifier Michael Unterbuchner.
The tournament will be broadcast live on Sky Sports and through the PDC’s worldwide broadcast partners, as well as through PDCTV-HD for Rest of the World Subscribers.
2018 bwin Grand Slam of Darts
Friday, November 16
Mensur Suljovic 16-9 Dimitri Van den Bergh
Gerwyn Price 16-15 Simon Whitlock
Saturday, November 17 (1900 GMT)
Michael Unterbuchner v Gary Anderson
Jonny Clayton v Michael van Gerwen
Sunday, November 18
Afternoon Session (1300 GMT)
Gerwyn Price v Mensur Suljovic
Clayton/Van Gerwen v Unterbuchner/Anderson
Evening Session (1930 GMT)