Goalie Andrei Vasilevskiy made 35 saves in the win for his third Stanley Cup Playoff victory.
There has been no change in the status of No. 1 goalie Ben Bishop, who has been out since sustaining a lower-body injury in Game 1 on May 13, Cooper said. The Lightning coach said a decision on whether Bishop will play again in the series will come once he is cleared.
Pittsburgh also is facing a potential goalie change after rookie Matt Murray was pulled in Game 4. Marc-Andre Fleury, who hadn't played since March 31 after sustaining his second concussion of the season, made seven saves in relief Friday.
"I think [Fleury's] been their franchise goalie for a number of years, and I don't think it really changes anything, because ultimately they're playing with a guy [Murray] that was on fire," Cooper said. "He's carried them to this point.
"So I think whatever decision they make, you've still got to put the puck behind them, and they're both really good National Hockey League goalies. So it doesn't change our mindset at all. You've still got to find a way to get it behind them."
The Lightning are 3-3 in Game 5 over the past two playoffs and are 1-2 on the road. The road win came in the 2015 Eastern Conference Final against the New York Rangers at Madison Square Garden.
"I think it's always hard to play in the opposing buildings," Tampa Bay defenseman Jason Garrison said. "And I don't think it's going to be any different. It's usually the same. I think we know what to expect in their building, and I don't think it's going to be any different than the way that they played there the last few games."