"They are a good team and they are going to take advantage of their chances," Rangers forward Mika Zibanejad said. "That's what happened."
Ondrej Pavelec made 42 saves for New York (33-36-9), which was eliminated from Stanley Cup Playoff contention Tuesday.
"If you look at tonight, it's kind of a microcosm for a lot of the games for us," Rangers forward Chris Kreider said. "We're playing a really good team that you know if you have lapses, they're going to capitalize."
Brady Skjei scored at 14:59 of the first period to give the Rangers a 1-0 lead.
Paquette made it 1-1 at 3:15 of the second period, with Miller getting an assist. He has 16 points (nine goals, seven assists) in 15 games with Tampa Bay.
"Tough game. We go from last night (against the Bruins) to tonight," Lightning captain Steven Stamkos said. "There's obviously a little different feel in the game and atmosphere, so to get the win was nice."
Killorn gave the Lightning a 2-1 lead at 4:33 of the second off his rebound.
Filip Chytil scored his first NHL goal, in his fifth game, at 8:14 of the third period to make it 5-2, and Kreider scored at 16:31 to make it 5-3.