Welshman Price averaged 100.82 in the annual double-start tournament at the Morningside Arena in Leicester.
The world number one hit six 180s in nine legs and checked out on 81 after Smith had missed three doubles to force a deciding set.
“I think I played pretty well, Michael didn’t play too bad either, but I was pretty consistent,” world champion Price told Sky Sports after his 2-0 win.
“He bombed an opportunity in that last leg and I took it.
“I knew it was going to be a tough game. Everybody’s out there to beat me and I don’t blame them.
“I’m playing really well and I just thrive in these situations. Under pressure I’m playing some good darts.”
Two-time champion James Wade produced a bullseye finish for a 121 sudden-death leg checkout against Australian Damon Heta.
Heta surged into a 2-0 lead in the first set and hit a second 180 in the third leg.
But missed doubles proved costly and number four seed Wade rattled off three legs to take the set.
Heta levelled to take the match into a third set and it went all the way before Wade won the fifth leg decider.
Daryl Gurney the 2017 champion, lost 2-0 to Stephen Bunting and Mervyn King beat Martijn Kleermaker by the same scoreline.
Ross Smith marked his first Grand Prix appearance with a 2-0 victory over fellow Englishman Joe Cullen.
“I think the doubles went well from the start so I’m very happy,” Smith said.
“I’ve had a lot of mates who’ve helped me out with the practice side of it.
“They’ve kept me on the dartboard in the last three or four weeks, so I have to thank my mates for that.”
Dave Chisnall beat Mensur Suljovic 2-1, Luke Humphries overcame Dirk Van Duijvenbode 2-0 and Ryan Searle defeated Dimitri Van Den Bergh 2-1 in another match decided by a sudden death leg.