Rovers roared into a 3-0 half-time lead thanks to goals from Jordan Rhodes, Grant Hanley and Rudy Gestede, and were comfortably seeing out the match until the decision to award the visitors a penalty nine minutes from time.
The referee ruled that Baptiste had brought down Cherries man Adam Smith in the area when no contact appeared to be made. Brett Pitman converted from the spot before Steve Cook reduced the scoreline further on 90 minutes.
As the visitors poured forward bodies were thrown in front of the ball, Baptiste in particular making one huge block in the closing seconds to ensure Rovers claimed the points.
"The main thing is we got three points against a very very good side," Baptiste told Radio Rovers after the game.
"You saw in the first 45 minutes, we were unbelievable, we could have been 5-0 up, the lads up top were brilliant.
"Then they get the decision and it is a killer because I haven't even touched him, that is the worse thing, and it completely changed the game. At first I thought he was going to be booked.
"Thankfully this one didn't cost us, it is a massive win, they'll be up there this year Bournemouth are an excellent team.
"We now have a massive game against Wolves next Saturday, if we can get three points there then it will have been an unbelievable start."
Supporters are reminded that tickets for the Wolves match at Molineux have to be purchased from Rovers in advanced as no tickets will be available on the day.
Prices are £27 Adults, £15 Seniors/u21s, £12 u17s and £10 u10s. Buy online today at www.onerovers.co.uk