Goals in each half from Michael Smith and Richard Wood saw the Millers to a 2-0 success at Ashton Gate, lifting the South Yorkshiremen to within three points of Championship safety.
After more than half of their playing and coaching staff tested positive for coronavirus, Rotherham were forced to close their training ground at the start of the month and went 13 days without a match before returning to action against Watford in midweek.
That game ended in a 4-1 defeat, but the Millers got back to winning ways on Saturday, despite the fact that a number of the players who lined up to take on the Robins were still struggling with Covid after-effects.
"It has been an unbelievably difficult two weeks," reflected Barker, standing in for manager Paul Warne, who remains in self-isolation.
"Obviously there has been a massive amount of illness. Some players are probably playing when they’re not quite ready to.
"But, like I say all the time, as a group of players they are absolutely fantastic.
"You ask them to play, you ask them to give you their all and they get on with it every week, every day in training.
"This was a great effort from the players."
Smith put the Millers in front on 44 minutes, beating onrushing City goalkeeper Daniel Bentley to Wes Harding's inviting right-wing cross and nodding into the unguarded net.
Captain Wood then wrapped things up 17 minutes from time when his header from a Dan Barlaser corner was deflected home by a Robins defender.
"It's a massive win, a massive clean-sheet and it was massively important that we signed off for this international break with a win," assistant manager Barker added.
“It makes the league table look a lot more attractive for the next two weeks.
"I thought the lads were excellent, so I'm pleased for them as a group of people because their work ethic on a daily basis is fantastic."
Victory moves Rotherham to within three points of 21st-placed Birmingham, with three games in hand.
Bristol City: Bentley; Hunt (Pearson 78), Mariappa, Kalas (Vyner 27), Sessegnon; Massengo (Bell 79), Walsh; Wells, Palmer (Lansbury 60), O’Dowda; Diedhiou (Semenyo 60). Unused substitutes: O’Leary, Nagy, Barkinson, Towler.
Rotherham United: Johansson; Ihiekwe, Wood, A MacDonald; Harding, Wing (Clarke 88), Barlaser (S MacDonald 88), Crooks, Giles (Olosunde 65); Ladapo (Jozefzoon 75), Smith (Hirst 87). Unused substitutes: Blackman, Wiles, Sadlier.
Referee: M Donohue (Greater Manchester).