The Robins' new signing, Sam Baldock, was paraded before the Ashton Gate faithful at the break following his move from West Ham on a three-year deal for an undisclosed fee.
But he may find it hard to break into Derek McInnes' starting XI on this showing.
Both sides were keen to hit back after opening-day defeats, City at Nottingham Forest and Palace having been denied late on in a 3-2 defeat by Watford.
And it was Palace who were first to show when Wilfried Zaha's 20-yard effort was saved by Tom Heaton after just four minutes.
The Robins were stung into action and Jon Stead rattled the woodwork with a header before the striker provided the assist for Ryan Taylor to hammer home the hosts' first after only nine minutes.
Palace were reeling and were hit by a second only three minutes later. This time it was Martyn Woolford who registered, hitting home left-footed from 12 yards out.
It looked like a damage limitation exercise for the visitors at this point but Dougie Freedman's side were putting in plenty of effort and Dean Moxey joined City's Richard Foster in the book for an over-zealous challenge on Albert Adomah after 33 minutes.
Stead should have put the game to bed a minute later but Julian Speroni in the Palace goal saved the striker's six-yard effort with his feet.
Palace's Kagisho Dikgacoi joined team-mate Moxey in referee Michael Naylor's book following a challenge on City's Greg Cunningham six minutes from the break.
Palace needed to get a goal back quickly after half-time and Joel Ward signalled their intentions, striking over the bar from 18 yards.
Aaron Wilbraham also tried his luck, this time from 30 yards, but his effort sailed harmlessly wide of Heaton's goal.
Palace's Louis Carey was booked for a challenge on Wilbraham after 55 minutes, but the game was effectively over four minutes later when another foul, this time by Jonathan Parr on Stead in the penalty area, led to a spot-kick which was easily despatched by Stead to make it 3-0.
Palace continued to press, though, and were rewarded for their efforts with 26 minutes left when Dikgacoi struck home after good work from Owen Garvan and Wilbraham.
But any chance of a late Palace comeback was finally snuffed out by Adomah with nine minutes left when he hammered home in impressive fashion from 25 yards to complete the home side's rout.