The 24-year-old had his serve working, pounding his Finnish counterpart with 29 aces in the match.
Pospisil is looking to repeat the success he had in Switzerland last year, which saw him reach the semifinal.
He lost that match to Roger Federer, despite forcing a deciding third set.
Pospisil, who is ranked 44th in the world, will likely have a tough test in the second round. He will play the winner between Bulgaria's Grigor Dimitrov and Alexander Zverev of Germany.
Dimitrov has claimed three titles this season, and currently is the No. 11 ranked player on tour. Meanwhile, Zverev entered the tournament as a wild card.
Pospisil and Dimitrov have never faced each other.