The Penguins, who trail in a playoff series for the first time all postseason, will go with Murray over Marc-Andre Fleury, who allowed four goals on nine shots in a 5-1 loss in Game 3 on Wednesday night as the Senators took a 2-1 series lead.
"That's been a hard decision for this coaching staff all year long," Sullivan told reporters Friday morning. "As I said yesterday, it's a good difficult decision to have because we have two guys who are as capable as they are. Both of these guys have helped this team win all year long. They're both high-quality people and they're high-quality goaltenders. We never take these decisions lightly. They're extremely difficult decisions. This is the choice that we made for Game 4."
Murray allowed one goal the rest of the way after replacing Fleury in Game 3.
This will be Murray's first start of the postseason due to a lower-body injury he re-aggravated during warmup before the first game of the playoffs against the Columbus Blue Jackets.
A year ago in the playoffs, the 22-year-old Murray helped lead the Penguins to a Stanley Cup with a 15-6 record, posting a .923 save percentage.
Both goalies skated Friday morning at the University of Ottawa's Minto Sports Complex.
Fleury, 32, has a 9-6 record with a .924 save percentage in the postseason.
"Marc was a professional like he always is," Sullivan said of Fleury being told of the decision. "Both of these guys handled the decision we made extremely professional. As we always say to them, these guys are both competitors. They both want to be in the net. We don't always expect them to agree with our decisions.
"Our hope is that they respect our decision. Both of them have always been professional. They're competitors. I understand. They want to be in the net. That's what makes them as good as they are. As I said, these decisions are very difficult. That's the choice that we made."
Also out Friday night for the Penguins will be defenseman Justin Schultz (upper-body injury) and forwards Bryan Rust (upper body), Patric Hornqvist (upper body) and Tom Kuhnhackl (lower body).