Tampa Bay scored twice before the game was 90 seconds old, breaking the ice on a marker by Brandon Hagel before Charle-Edouard D'Astous extended the advantage at 1:26.
Zemgus Girgensons made it 3-0 at the 5:52 mark when his shot from the left wing caromed in off a stick, prompting Devin Cooley to come on in relief of starting netminder Dustin Wolf.
Declan Carlile added a fourth for Tampa Bay, who took a 4-0 lead into the intermission.
Cooley was strong between the pipes from then on; his second-period stops included a sliding robbery of an Oliver Bjorkstand one-timer near the midway mark, then a tumbling series of arm saves off Nick Paul on a Lightning powerplay about five minutes later.
Farabee got one back for Calgary, snapping a puck past Andrei Vasilevskiy off the rush 1:04 into period three, marking his fourth goal in as many contests.