The 24-year-old striker, who joined Celtic from Schalke last August, has been in superb form during the Parkhead club's pre-season tour of Austria and his treble came just 48 hours after his second-half strike against Rapid Vienna.
The Finn's opening goal cancelled out Dragan Vujanovic's opener for the hosts, and he followed up with another two strikes from close range after the interval.
Amido Balde and Leigh Griffiths added to the Parkhead side's total as they powered to an easy victory, and the only blemish for the Scottish side was a red card for teenager Liam Henderson midway through the second half.
"I'm really pleased - it was a good game, with goals," said Pukki, on Celtic TV. "This helps me and I just hope to keep going. The competitive games are coming soon, and hopefully I can be part of the team and keep scoring.
"The first half we didn't play as well as we can, but we still managed to score and it was 1-1 and it was good to kick on in the second half. "As a striker, I have to work hard for the team and that's what helps the rest of the side," he added.