Playing in his fourth career game, Cirelli scored Tampa Bay's third goal and assisted on its second goal and fourth goal.
Cedric Paquette and Adam Erne scored in the first period when the Lightning took a two-goal lead before the Rangers even registered a shot on goal.
Chris Kunitz scored Tampa Bay's fourth goal after getting the assist on Paquette's tally. Tyler Johnson scored the final goal for the Lighting.
Andrei Vasilevskiy made 27 saves and became the first goaltender to reach 40 wins.
Tampa Bay won its fourth straight and gained a point in its ninth straight contest (8-0-1).
Ryan Spooner scored and had two assists for the Rangers, who dropped their second straight.
Mats Zuccarello and Kevin Hayes netted the other New York goals.
Henrik Lundqvist allowed four goals on 31 shots before getting pulled with 7:25 left in the second.
The Lightning took the lead 2:30 into the game shortly after Rangers defenseman John Gilmour coughed up the puck in the neutral zone. Ryan Callahan dished to Kunitz, who sped down on a 2-on-1 and fired a shot off Lundqvist's left shoulder. Paquette tapped the rebound into the vacated net.
Tampa Bay made it 2-0 when Erne scored his third goal off another Rangers turnover by Ryan Spooner. Erne gained possession and scored from the low slot while falling to the ice.
The Lightning extended the lead to 3-0 1:53 into the second on a tip-in by Cirelli, who scored his second career goal.
Spooner got the Rangers on the board by skating into the slot with 12:50 remaining, pouncing on a rebound and lifting it into the net.
Cirelli recorded his third point when Lundqvist mishandled the puck behind the net. Cirelli gained possession and hit Kunitz with a pass from behind the net for the easy goal.
Johnson scored the final goal late in the second, and Zuccarello made it 5-2 3:27 into the third. Hayes scored with 2:19 remaining on a tip-in.
--Field Level Media
NY Rangers | Tampa Bay | |
Ryan Spooner 3 | Points | Anthony Cirelli 3 |
Ryan Spooner 1 | Goals | Anthony Cirelli 1 |
Ryan Spooner 2 | Assists | Anthony Cirelli 2 |
N/A | Power Play Goals | N/A |
N/A | Short Handed Goals | N/A |
Alexandar Georgiev .929 | Save Percentage | Andrei Vasilevskiy .900 |
Henrik Lundqvist 27 | Saves | Andrei Vasilevskiy 27 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
NY Rangers | 30 | 3 | 0-3 | 4-4 | 8 | 28 |
Tampa Bay | 45 | 5 | 0-4 | 3-3 | 6 | 42 |