Rhodes got his 17th and 18th league goals for Rovers with an expert strike in each half.
First, he reacted quickest to latch on to a loose ball after a Morten Gamst Pedersen cross was not cleared and he moved left into space before firing into the opposite corner, the sixth consecutive game he has scored in.
In the second half, he raced onto a long Danny Murphy pass, showing great strength before slotting into the left corner from inside the area and Appleton was full of praise for Rhodes after winning his first league game as Rovers boss.
"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," Appleton said.
"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."