Sarcevic, a summer signing from non-league Chester FC, sent the Cod Army into half-time in control before further goals from Jamille Matt and substitute Matty Blair finished off the Gulls, who did pull a goal back through Elliot Benyon to make it 3-1.
Sarcevic opened his account for Graham Alexander's men after 10 minutes when he powered a header past goalkeeper Martin Rice from a Junior Brown cross.
The home side bossed the action and could have stretched their lead from a Steven Schumacher free-kick but Rice got down low to his left to push the shot round the post.
The Torquay keeper was having a busy afternoon and soon had to parry a Jamille Matt drive as Fleetwood pushed for a second goal.
It finally came seven minutes before the break as Sarcevic played a neat one-two with Jeff Hughes before letting rip from 20 yards to quickly double his Football League tally.
The visitors failed to test Fleetwood stopper Scott Davies in the opening 45 minutes and fell further behind two minutes after the hour mark.
The Gulls' defence made a hash of dealing with a corner, with Matt getting a shin on it in a crowded box and the ball trickled over the line.
Jordan Chapell finally forced Davies into action with 15 minutes to play. His cross caused a moment of panic as the Fleetwood keeper sent it spinning onto the top of the net.
A long-range effort from substitute Daniel Sullivan also forced a save from Davies as the home side took their foot off the gas.
And Alan Knill's men did grab a late consolation when sub Benyon slammed home a shot from the left channel.
But the home side responded immediately. David Ball crossed for Blair, on the pitch for a matter of seconds, to scramble home and restore the three-goal advantage.