However, the coach wanted to reiterate to his players they still have a lot of work to do in the last game of the series at Benchmark International Arena on Sunday (6 p.m. ET; The Spot, HBO MAX, truTV, TNT, SN, TVAS, CBC).
The Lightning extended the best-of-7 series with a 1-0 overtime win in Game 6 at Bell Centre in Montreal on Friday.
"In the locker room after the game, sure guys were pumped, but we haven't won anything yet," Cooper said. "All we did was win a game to send this back to Tampa and keep our season alive.
“You don't want to rain on the parade, because what a hell of a win by the guys. But we haven't accomplished anything yet. We've just pushed a game."
The Lightning have fared well in win-or-go-home situations since Cooper arrived in 2013. Tampa Bay is 4-2, including 2-1 at home, in Game 7s during his tenure as coach. Tampa Bay has won its past two, including 2-1 at the Toronto Maple Leafs in a 2022 first-round series, and 1-0 here against the New York Islanders in the 2021 conference finals.
All six games in this series have been decided by one goal and four have required overtime with each team winning twice in the extra period. Gage Goncalves won Game 6 at 9:03.
"It's been unreal, to be honest; we both had 106 points coming into this series," said Tampa Bay forward Brandon Hagel, who has eight points (six goals, two assists) in six games. "They're a really, really good hockey team over there and we're a really, really good hockey team here.
“I don't think we expected anything else other than what's been going on here. They've got everything over there and we think we've got everything over here."