Wanderers were second best and looked like going down to Will Vaulks' second-half free-kick - but Doidge stepped up in the 85th minute to open his account against the club that tried to sign him last summer.
It was a point that Phil Parkinson's men, who missed an earlier penalty, barely deserved as Rotherham dominated and had enough chances to have put the game to bed.
Vaulks' strike put them ahead in the 56th minute but Michael Smith hit the post and missed other key chances to extend the lead while Ryan Williams put a free header wide.
It means Paul Warne's men have now gone six games without a win, although they are undefeated in five at the AESSEAL New York Stadium.
The Millers had not won since the resumption of the last international break in September and they meant business from the off, creating several chances in the opening 15 minutes.
Semi Ajayi headed a second-minute corner just wide and Smith, without a goal since the second game of the season, drilled an effort over before heading Jon Taylor's cross straight at Ben Alnwick.
The home domination continued and after Taylor had an effort deflected onto the near post, Kyle Vassell had the chance of the half - but he could not connect properly with a free header in the six-yard box.
Rotherham should have paid for their wastefulness early into the second half after Richard Wood clumsily fouled Josh Magennis, but keeper Rodak produced a brilliant save to keep out Magennis' penalty.
Soon after, the Millers got their goal their first-half play had deserved and it was a cracker as Vaulks blasted a low 25-yard free-kick into the bottom corner.
They had further chances to extend their lead but Smith shot straight at Alnwick and Ryan Williams headed wide from a good position.
It was all Rotherham and Smith's quest to get onto the scoreline continued and he came close - but a 25-yard curling effort crashed into the post with Alnwick beaten.
The failure to increase their lead proved costly five minutes from the end as Bolton equalised out of nowhere.
Joe Mattock allowed a long ball to bounce, Clayton Donaldson took advantage by playing in Doidge, who crashed home from the edge of the area for his first goal since joining from Forest Green.
Warne felt his side deserved to win but was pragmatic: "Disappointed not to win, even more so because their goal was so late on," he said.
"I never think that, I am a bit more experienced, until the whistle goes I am virtually having a heart attack.
"They had four strikers on the pitch so I knew they would create something.
"It's a pity we didn't get a second goal. I thought we created two really good chances from set-pieces, on another day they go in and we take three points."
Bolton boss Phil Parkinson praised his side's character but felt it could have been a different game had Magennis scored his penalty early in the second half.
"It is a tough place to come and Rotherham have proved that this season, with games against Derby and Stoke," he said.
"They put the ball into the box and it is a difficult place to come.
"I thought the penalty was a turning point in the game. We started the second half very well and had the chance to go in front.
"The penalty miss, it was a great save, was a key moment and it gave them a great lift, the crowd got behind them and they went on to dominate.
"You have got to give our lads credit, 1-0 down to respond in the way we did. We wanted three points but we will definitely take a point."