Tomer Hemed supplied two goals and scored a third as Chris Hughton's side bounced back from defeat at Cardiff.
Jamie Murphy and former City striker Sam Baldock had the Seagulls two ahead early on before Hemed latched on to Beram Kayal's ball for the third goal.
Mark Little deflected the fourth into his own net, while Kieran Agard hit the crossbar with a late penalty for City.
Victory for Brighton keeps them fourth in the table on an evening when the division's top four sides all won.
Media playback is not supported on this device
Hemed, a summer arrival from Almeria, scored his ninth league goal of the season to effectively wrap up the points on 56 minutes.
He had already showed his creative side for Murphy's early finish from inside the area, and then Baldock's low drive from the edge of the box in the first half.
The Israel international also went close to a second goal when he drilled a long-range shot just over the bar.
On a night to forget for Lee Johnson and his side, they were denied a stoppage-time consolation from the spot when Agard could only strike the bar from 12 yards.
Bristol City head coach Lee Johnson:
"It was a frustrating night. We huffed and we puffed to try and blow their house down, but theirs was made of brick and ours was made of paper.
"It disappointed me that we ran out of ideas after Brighton's first goal and there are no excuses. We weren't good enough on the night.
"There is a positive in the fact that the bottom three all lost and another round of games has gone by, but we want to be looking up the table."
Brighton manager Chris Hughton:
"I was delighted the penalty didn't go in at the end because it would have put a damper on a near-perfect team performance.
"We had to improve because the display at Cardiff wasn't good enough and Bristol have been in good form and we only won comfortably because we did everything right.
"It was as complete a performance as we have put in all season. We are not a team who scores a lot of goals so to get four was very pleasing."
Brighton got their Championship promotion push back on track with an emphatic win at Bristol City.