Silva's moment of quality settled an otherwise scrappy contest on Trentside but Forest won't care about the entertainment value having earned three points which moved them back above Fulham into fourth place in the Sky Bet Championship.
Sabri Lamouchi made one change from the weekend win over Huddersfield Town as Ryan Yates replaced Brennan Johnson in the Forest midfield while Samba Sow returned to action with a place on the substitutes' bench.
There was a lengthy stoppage in the opening minutes of the contest as City's Callum O'Dowda received treatment following a collision with Matty Cash before Benik Afobe had the first shot on target of the night as his low effort from the edge of the box was comfortably held by Brice Samba.
Afobe was causing problems inside the Forest penalty area and the former Wolves striker almost found the opening goal on 14 minutes but his header from Nahki Wells' cross was planted just wide of Samba's right-hand post.
Forest burst into life ten minutes before half-time with their best effort of the evening so far. Having initially tripped over the ball, Lolley worked exceptionally hard to keep hold of it and played a pass inside to Cash. The youngster powered a strike towards goal which Bentley got down well to turn behind for a corner.
The Reds made the breakthrough on 63 minutes thanks to Silva's sumptuous free-kick. Yates had his legs hacked from under him on the edge of the 'D' and the Portuguese stepped up to curl a terrific strike over the wall and into the back of Daniel Bentley's net.
Play-off chasing City have a number of talented youngsters in their ranks but it was one of their most experienced players who saw red on 78 minutes. Referee Darren Bond had already stopped play just inside the visitors' half when Williams pushed Yuri Ribeiro in the face and the Welsh international was shown a straight red card.
Having found the all-important goal, Forest were able to see out seven minutes of stoppage time at the end of the evening to claim a crucial victory and some much-needed momentum heading into Saturday's East Midlands derby at Pride Park.
Forest: Samba; Cash, Figueiredo, Worrall, Ribeiro; Watson (c), Yates (Sow 88'); Lolley (Da Costa 46'), Silva (Dawson 88'), Ameobi; Grabban (Walker 90')
Subs not used: Smith, Carvalho, Bostock, Jenkinson, Mighten
Goal: Silva 63'
Bristol City: Maenpaa (Bentley 27'); Vyner, Williams, Baker, Dasilva; O'Dowda (Paterson 76'), Smith (c), Nagy, Weimann (Palmer 76'); Afobe, Wells (Diedhiou 64')
Subs not used: Watkins, Kalas, Rowe, Benkovic, Massengo
Bookings: Weimann 45', Vyner 84'
Sent off: Williams 78'
Referee: Darren Bond
