The Robins surged into a 3-0 interval lead thanks to Phil Jevons' hat-trick, but had to withstand a battling comeback by their League One rivals before clinching their place in the last 64 of the competition.
Former Everton trainee Jevons only moved to Ashton Gate from Yeovil Town in the summer, but brought his goal tally for the season up to 11 with a stunning individual display in the opening 45 minutes.
The 27-year-old broke the deadlock in the 21st minute when he latched on to Cole Skuse's pass before curling a shot home.
Two more Jevons goals just before the break appeared to have killed off the Gills, but the visitors produced a spirited second-half display.
In the 49th minute Gary Mulligan volleyed home, only for Enoch Showunmi to restore City's three-goal advantage in the 64th minute with a powerful drive.
Back came Ronnie Jepson's side and, two minutes later, Michael Flynn headed home to make it 4-2.
Flynn scored from the penalty spot in the last minute but it was too little too late for the visitors as Bristol City earned the right to host Coventry City in the third round.