The evergreen Brown, 36, led the way with two tries as the Red Devils recovered from a half-time deficit to thrash winless Leigh 34-8 at the AJ Bell Stadium.
Former New Zealand and Samoa international Krisnan Inu, 34, was also instrumental in the result as he kicked five goals and pulled off a sensational interception to set up a breakaway try for Ken Sio.
Marshall said: “Kev was fantastic for us. I’m really happy for him. He’s had a tough week.
“His dad was poorly at the start of the week but, fingers crossed, he’s doing really well now.
“He showed magnificent leadership and we’re fortunate he’s put his hand up to go around again this year.
“I thought all our leaders, all our key players, really stood up. You learn a lot about yourselves when you lose a few games and we’re really fortunate to have these experienced players.”
It was Salford’s first Super League win of the season at the fourth attempt, and Marshall’s first since taking over as head coach.
He said: “We’re all in it together. It’s not about me. For the club and the fans, we owed them a performance.
“We’re really pleased. I never wavered or doubted the team. I knew we’d come through.
“It wasn’t fluid and there is a lot of improvement to come, but we had the resilience and toughness to come through.”
Marshall added the one notable downside was the loss of centre Matt Costello with a “significant shoulder injury”.