The Eagles began the game on top, though their first effort at goal was mis-hit by Chinese Taipei international Will Donkin. Responding with their own effort within the game's opening 10 minutes, however, Bristol applied pressure to the Palace backline via Jamie Taylor, whose shot was deflected and sent spinning out for a corner.
City then sustained a period of play on top, and Vince Harper attempted to net the Robins' first of several efforts but saw his shot at goal held by Palace 'keeper Rohan Luthra.
Next up was Marcus Day, who turned well on the ball only to rifle it over the visitor's bar. Luthra was then called into action again as he was forced to respond to a Taylor strike, which he got behind well to maintain his indomitability.
Having soaked up the home side's pressure, the Eagles then responded after 20 minutes when David Omilabu tested City's Will Buse for the first time. Their regained presence in the game was swiftly rewarded when Aveiro responded fastest to a loose ball in the box following Donkin's saved effort, and the Palace winger tapped home calmly.
Bristol looked to equalise immediately, and were only stopped by Luthra as he struck out a strong leg to deny Sam Bell. The Palace backline were again thanking Luthra when his reflexes kept the home side from opening their account for the day as he saved Taylor's well-struck volley.
Following the half-time break, City finally found themselves level when Zak Smith played the ball through to Day, who found the back of the net after 51 minutes.
In a quieter second-half, though, Palace managed to grasp the lead again as Keutcha bundled the ball over the line following a packed Bristol area trying in vain to defend an Eagles free-kick.
The goal seemed to kill-off any hopes of the home side taking a point and Palace saw the game out to grab a win in southwest England.
Palace: Luthra, Russell (Boateng 59), Chamberlin-Gayle, Gurung, Onoabhagbe, Siddick, Keutcha, Boateng, Omilabu (Kymani-Gordon 79), Donkin (Parris 89), Aveiro.
Subs: Trehy, Russell, Parris.
Bristol: Buse, Gould, James Taylor (Towler 58), Owers, Low, Pearson, Jamie Taylor, Smith, Bell, Day, Harper.
Subs: Sainsbury, Allen, Benarous, Henry.