Jacob Mellis' near-post effort gave Barnsley a deserved lead, but Rhodes turned and shot to pull the two sides level, then Nuno Gomes tapped in to maintain Blackburn's 100% home record.
Rhodes now has three from three games since his move to Blackburn and Kean is delighted with the club's investment.
Kean said: "I must be very honest. I thought we were dreadful in the first half. We were well under the standards we set. We didn't pass the ball well enough in any areas of the pitch.
"At times like that you're looking for special players to produce something to get you back in the game and that's what Jordan did because Barnsley were far better than us in the first half.
"I've been impressed with his hold up play and his retention of information. In times when we're under the cosh and struggling in the game, if he can get one or two chances, he's going to scare the living daylights out of any defenders because his ratio of chances to goals is going to be so high."