Boeser gave the Canucks a 2-1 lead on with an unassisted marker on a slap shot off a Tampa Bay giveaway. It was the first goal of 2018-19 for Boeser, who led the Canucks in scoring as a rookie last season but had struggled in his first three games of the current campaign.
Rookie Elias Pettersson, with his team-leading fourth goal of the season, Jake Virtanen and Markus Granlund also tallied for the Canucks.
Brayden Point scored for Tampa Bay.
Vancouver goaltender Anders Nilsson posted 33 saves as the Lightning outshot the Canucks 34-28.
Canucks coach Travis Green gave the backup goaltender his first start of the season. Nilsson's job security has been questioned after he posted a poor 7-14-4 record and .901 save percentage last season. But Nilsson, displaying a more upright stance rather than the extremely low crouch he displayed last season, was steady and could not be faulted on the only goal he allowed.
Tyler Johnson made his season debut for the Lightning after missing the first game due to an upper-body injury that has bothered him for the past two weeks. Normally a centre, he played wing on the second line with Point and Yanni Gourde.
Johnson's hard work helped the Lightning get on the scoreboard first. His attempts to dig for the puck in front of the Vancouver net led to Point's goal on a one-timer off a short pass from Gourde following a rebound.
Pettersson drew the Canucks even at 11:07 of the third period as he deflected Derrick Pouliot's shot in mid-air.
A minute and 10 seconds later, Boeser gave the Canucks their first lead of the game before Virtanen and Granlund rounded out the scoring with empty-net tallies in the last two minutes. Virtanen, who has called upon by Green to produce more offence, also recorded an assist.
(With inputs from agencies.)