Aden Flint headed against the post for City before Baldock put them ahead, controlling Bobby Reid's pass in the box to lash a fine strike into the top corner for his fourth goal of the season.
The Dons had plenty of possession in the first half, but they struggled to unlock the Robins' defence, with Bamford firing their best chance into the side-netting from a tight angle.
Bamford equalised for the Dons seven minutes after the break when he raced on to Luke Chadwick's pass and drilled a clinical left-footed shot inside the far post.
Baldock restored City's lead in the 66th minute when he ran clear on to a long punt and drilled the ball low past Dons' goalkeeper David Martin.
But Carruthers made it it 2-2 just three minutes later, firing a first-time shot into the top corner from substitute Dele Alli's pass.
- Sports & Recreation
- Patrick Bamford
- Samir Carruthers