The Pars got off to an excellent start, scoring the opener after just eight minutes when Clark collected a pass from Declan McManus, made ground down the right and moved inside before drilling a fierce drive past Graeme Smith in the City goal.
Dunfermline doubled their lead just a minute later when Clark grabbed his second, firing a shot from 15 yards into the bottom corner.
City battled back and Kalvin Orsi saw a close-range drive blocked by Kallum Higginbotham in the 21st minute before a 25-yard drive from Willie Dyer was tipped away by Lee Robinson in the Dunfermline goal.
Callum Tapping then had a long-range effort held by Robinson in the 34th minute before the last two chances of the half fell Dunfermline’s way in the final five minutes when McManus curled a drive just wide of the target and then saw a close-range shot hit the top of the bar before being cleared.
The opening stages of the second half were evenly balanced but it was the visitors who scored the decisive third goal and wrapped up the points when Sunderland loanee Tom Beadling played a delightful through ball to Clark, who made no mistake from the edge of the box to complete his hat-trick.
Clark, pictured, very nearly grabbed his fourth soon after when he sent an 18-yard shot inches wide of the post.
Dunfermline were now in total control and it should have been 4-0 in the 72nd minute when substitute Daniel Armstrong, who had replaced McManus a couple of minutes earlier, was clean through on goal but steered his shot wide of the target.