Last year’s League One champions entered the clash on the back of a frustrating start to life in the second tier, collecting just a single point from the first three games.
Yet there was no sign of panic early on at the Riverside as they took the lead through Bryan’s well-taken goal which earned them a 1-0 win.
Indeed, it took two fine first-half saves from Dimi Konstantopoulos just to keep Boro in the game, Aaron Wilbraham and Jonathan Kodjia were the men denied.
Perhaps inspired by his opposite number, City goalkeeper Ben Hamer proved in similar form during the second period as he spectacularly denied Daniel Ayala and Grant Leadbitter amid a fine response from the hosts.
Aitor Karanka’s men would leave empty-handed, however, as the Robins held on to claim a precious three points.
The game started in a lively manner as both sides showed attacking verve, Stewart Downing striking just wide from 20 yards in the seventh minute.
But it was City who took the lead moments later after superb interchange between Bobby Reid, Wilbraham and Bryan.
The trio worked the ball into an opening, with their neat play ending when Bryan collected Wilbraham’s pass, cut inside and curled a pinpoint effort beyond Konstantopoulos and into the top corner.
Boro responded solidly as Cristhian Stuani and Yanic Wildschut threatened either side of a Downing volley being disallowed.
The Robins continued to look threatening, however, and should have moved 2-0 ahead in the 17th minute.
Konstantopoulos brilliantly denied Wilbraham from Kodjia’s pull-back before Reid somehow blazed over from six yards.
The Middlesbrough goalkeeper had to be on high alert again in the 30th minute when turning Kodjia’s powerful effort wide.
Downing continued to look the most likely player in red to spark a turnaround, epitomised by him narrowly missing the target from 20 yards.
Boro introduced Diego Fabbrini at half-time and the move impacted the game as the Italian pulled the strings during a good spell.
Yet Bristol City were withstanding increasing pressure, Hamer’s fingertips somehow keeping out Ayala’s header.
The shot-stopper produced an even better save midway through the second period when, having seemingly been wrong-footed, he got down low to deny Leadbitter.
Middlesbrough continued to look dangerous thereafter, although they were given a reminder of City’s threat as Bryan tested Konstantopoulos.
And that proved the last opportunity of note for either team, with Steve Cotterill’s side hanging on the take the spoils.