Danny Batth got the visitors off to a great start with a diving header after 10 minutes, but Nouha Dicko immediately scored an equaliser.
Kieran Agard headed Rotherham into the lead after 37 minutes from Ben Pringle's cross and Steve Evans' men went further ahead through Dicko's second goal of the game early in the second half.
But referee Michael Oliver threw Wolves a lifeline just before the hour mark with a controversial penalty decision, and Bakery Sako netted the spot-kick.
And Wanderers took full advantage, with James Henry running through the heart of the home defence after 64 minutes and firing past goalkeeper Adam Collin
Jackett said: "Both sides set out to attack from start to finish and there were some terrific goals.
"We did very well, I always thought we were in the game and at 3-1 down we got our game going right. I think we can score and be a threat constantly and going into the final 10 or 15 minutes we were looking for a winner not settling for a point.
"I was very pleased with the attitude and the character. We came back and got what looks to be a very good point away from home.
"We did very well and we dug deep at a tough place that was buzzing with a terrific atmosphere. It certainly was a big game for Rotherham and you could see it. The atmosphere was electric and the players were up for it.
"But we matched that and I didn't think we were ever out of the game. We've got two games at home now and we want to capitalise on that."