The Ghanian found the top corner from 18 yards before Steven Davies added a second shortly after the break as City continued their unbeaten run at Ashton Gate since Sean O'Driscoll took charge.
The Robins started brightly when Marvin Elliott teed up Neil Kilkenny but Boro goalkeeper Jason Steele kept out his curling effort from distance.
City did find a way past the Boro keeper just after the half hour mark though with one of the best goals the strugglers have scored this season.
Kilkenny's raking 40-yard pass found Adomah and after taking on George Friend he cut inside and curled the ball into the top corner via the inside of the post for his fifth goal of the season.
Tony Mowbray's men, looking to close the two-point gap between themselves and the play-off places, did carve out a chance before the break but former Bristol Rovers man Mustapha Carayol fired over the crossbar.
But it only took seven second-half minutes for the Robins to double their lead when Davies was slipped in by Stephen Pearson after a quickly taken free-kick and he lashed the ball home from an angle to delight the Ashton Gate faithful.
Mowbray responded almost instantly, introducing Curtis Main for Marvin Emnes, as their hopes of a first away win of 2013 continued to fade.
And Main took just three minutes to threaten but his right-footed shot was blocked by Kilkenny.
At the other end the City supporters were furious that they were not awarded a penalty when they felt Davies' shot hit Rhys Williams' hand inside the box.
Adomah was continuing to shine for City and he carved out a 74th-minute chance for Elliott but the midfielder drilled a first-time effort wide. And then a minute later only the fingertips of Steele denied Davies his second of the afternoon after he went one-on-one with the keeper.
Steele continued to be in the thick of the action, denying Adomah as the winger looked to race around him as Boro failed to pick up three points on the road yet again.