An Alfie Dorrington own goal gave City an early lead before defender Guehi, a January signing from Crystal Palace, came off bench to seal the victory late on.
Pep Guardiola made several changes to his starting line-up with City still in with chance of catching league leaders Arsenal, and it led to a disjointed performance.
The hosts did take the lead in the sixth minute when Rayan Ait-Nouri's attempted cross from the left deflected off Salford defender Alfie Dorrington and into the back of the net.
Guardiola's charges had opportunities to extend the advantage with an Omar Marmoush volley ruled out for offside.
Salford had chances to get back into the contest, with the League Two side side testing hoe goalkeeper James Trafford.
With 65 minutes after the game gone, Guardiola made a triple substitution with Guehi, Antoine Semenyo and Nico OâReilly all entering the fray.
The changes seemed to give City more energy, especially in attack, and Guehi made it 2-0 after tapping in from a rebound after Rayan Cherki's cross was palmed away by the visiting shot-stopper.
The result means City, seven-time winners of this competition, are a step closer to a fourth-consecutive FA Cup final appearance.