This victory extended City's winning run in FA Cup home ties to 17, since they were knocked out by Championship club Middlesbrough in the fourth round in 2015.
That streak includes 77 goals and 11 clean sheets, but this was a scrappy performance by a club looking to reach a fourth FA Cup final in a row.
Salford, co-owned by former Manchester United stars Gary Neville and David Beckham, were in the tie right up until Guehi doubled the hosts' advantage in the 81st minute, and will take heart from this performance as they look to secure promotion to League One.
While Guardiola's side failed to hit top gear, there were still a couple of positives to take from this performance.
John Stones emerged from his first start since November unscathed, while Trafford - starting in place of regular number one Gianluigi Donnarumma - made a couple of decent saves as he looks to seal a place in the starting XI against Arsenal in next month's Carabao Cup final.
There was also Guehi's first Manchester City goal to celebrate, with the centre-half pouncing to help to ease some home nerves late on.