The brace means that Rhodes is now on 18 league goals for Rovers and his career tally moves onto one hundred.
Rhodes was on target against Bristol with a goal in each half, both showing what great skills he has as a finisher and he has got some Rovers fans already comparing him with the great Alan Shearer.
The goals also saw Appleton pick up his first league win since taking over at Ewood Park.
Which he thought was nice.
He told reporters after the game: "That's what he does. The first one sums him up in terms of how clinical he was. First touch with his right foot and to be as clinical as he was with his so-called weaker foot.
"With the second one, we've spoken about it a lot in the week. On the regain when we won the ball back we knew had to stretch Bristol as much as we possibly could and it worked.
"Jordan showed great persistence and strength and when he got an opportunity to get a strike at goal, I didn't think there'd be any other conclusion."
Appleton was also pleased with the defensive display of his team.
He added: "I don't want to keep harping on about it but I say to the players every week how important it is to keep clean sheets.
"If you do, you certainly can't lose a game of football and when you've got people like Kazim-Richards and Rhodes, you've got a good opportunity to try and get goals, so we're delighted at the minute."