Johnson could start again when the Penguins begin a three-game road trip against the Nashville Predators on Thursday night.
Pittsburgh (4-3-0) has won three straight after a rough start, during which Fleury went 0-3 while giving up 10 goals. Johnson has started each of his team's wins, the most recent a 5-2 victory over Ottawa on Monday.
"It's Flower's (Fleury's) team, everyone knows that," Johnson said. "It's important right now that if I am looked upon to get in there, I try to get the job done."
Coach Dan Bylsma wouldn't say who would get the nod Thursday, but indicated the No. 1 job remains Fleury's. He last played in a 4-3 loss to Toronto on Oct. 13 in which he gave up four goals on 14 shots.
"Flower's going to play 60-plus games and win a lot of hockey games for us," Bylsma said after practice Wednesday. "The way Johnny has played is that he stepped in and won some games for us, so we know that when he goes in there he's going to give us a great game."
Crosby had a goal and assist Monday and has recorded seven of his eight points in the last four games. Malkin, who scored his second goal of the season to go along with an assist, has five of his six points in his past four contests.
While the Penguins are heating up, Nashville (3-0-2) has suffered back-to-back overtime losses, falling 1-0 to Calgary on Tuesday.
Pekka Rinne returned after being injured in the third period of the season opener Oct. 9. He stopped 34 of 35 shots but was beaten by Rene Bourque in overtime.
"I've been practicing pretty well the last few days, and I only missed three games, so it was not a huge break," Rinne said. "I was a little more nervous than usual, but it was still a good game for me."
The Predators, 0 for 11 on the power play in the last two games after going 4 for 13 the first three contests, didn't get a shot on goal in the extra period.
Steve Sullivan has been held without a point the last two games after recording four goals and an assist in the previous three.
Nashville is trying to end its three-game homestand on a high note. It begins a stretch of 11 of 13 on the road Saturday.
The Predators may not be fully healthy when they do. Defenseman Ryan Suter left with a lower-body injury early in the first period Tuesday after colliding with a Calgary player.
"He might miss a little bit of time, but nothing major," coach Barry Trotz said.
Pittsburgh has been missing a defenseman, but Brooks Orpik (groin) is expected to return during the trip after sitting out five games.
Nashville is 9-4-0 with two ties all-time against Pittsburgh, taking the last two meetings. The Predators have won five straight at home in the series.