K'Andre Miller, Kaapo Kakko and Mika Zibanejad were the goalscorers for Rangers.
Nikita Kucherov, who opened the scoring in the 3rd minute, and Nicholas Paul were those of the Lightning.
As in match N.1, the victory for Rangers took a long time to emerge, Zibanejad only allowing his side to break away 3-1 at the start of the last third.
The Lightning players, who once again broke their teeth on New York goalkeeper Igor Shesterkin, author of 29 saves, came back to one length thanks to a goal from Nicholas Paul 2 minutes from the end.
But the Rangers held on until the end.
The winner of the series will meet in the Stanley Cup - the final of the NHL - the Edmonton Oilers or the Colorado Avalanche, opposed in the final to the West.
Wednesday June 1:
game N.1, NY Rangers - Tampa Bay Lightning 6-2
Friday June 3:
game N.2, NY Rangers - Tampa Bay Lightning 3-2
New York leads the series 2-0
Sunday, June 5: game N.3, Tampa Bay Lightning - NY Rangers
Tuesday, June 7: Game N.4, Tampa Bay Lightning - NY Rangers
Thursday, June 9: (if necessary) game N.5 NY Rangers - Tampa Bay Lightning
Saturday, June 11: (if necessary) game N.6, Tampa Bay Lightning - NY Rangers
Monday, June 13: (if necessary) game N.7, NY Rangers - Tampa Bay Lightning
NB: each series is played best of seven matches, the first team to achieve four wins advances to the next round
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