Murphy, signed in the summer from Fulham, scored his first goal for the club to put Rovers on the road to the fourth round.
Grant Hanley got the second on the hour mark as Blackburn chalked up their third straight victory.
Bowyer saluted his captain's response in the days following the sacking of Henning Berg.
"It was a great start for us and a good strike from Danny. Since myself and Terry (McPhillips) have come in and had to look after the team, Danny has been brilliant," Bowyer said.
"His support for us has been magnificent and we can't praise him enough.
"His goal was good and he reminded the lads yesterday that he's won the FA Cup with Liverpool so he's been great for the lads and he's been great for us. We'd be daft not to call on his experience."
Bowyer also responded to reports that West Ham have bid £2m for Martin Olsson and said more money would be needed.
"I haven't heard about the bid. It will have gone to the board first but in my opinion that is not enough.
"He's worth more than that. I wouldn't want to lose him. The football club needs him and we're striving to get back into the Premier League but if a good offer comes in, it's up for the board to decide."