Real dominated possession but found chances hard to come by, with Valencia keeper Stole Dimitrievski rarely called into action as the visitors struggled to turn control into threat.
It took them until the 65th minute to break the deadlock through Carreras before Mbappe wrapped up the points in stoppage time.
Barcelona lead the table on 58 points, with Real second on 57. Valencia are 17th, a point above the relegation zone.
Mbappe offered the main outlet with sporadic runs down the left but clear openings were limited.
Real coach Alvaro Arbeloa was forced to improvise, missing suspended winger Vinicius Jr and injured trio Jude Bellingham, Rodrygo and Eder Militao.
The absences opened the door for academy players Raul Asensio, David Jimenez and Gonzalo Garcia to start, with Mbappe providing the lone spark for an uninspiring Real side.
The deadlock was broken through fullback Carreras in a fortunate turn of events.
Making an ambitious run into the box, Carreras was dispossessed by Valencia’s defenders, but the attempted clearance ricocheted back off him and fortuitously fell at his feet.
The 22-year-old was quickest to react, sweeping a low shot into the bottom-left corner.
Valencia offered little in response and Real sealed the points in added time. Substitute Brahim Diaz launched a counter-attack down the left and slid a low cross into the area for Mbappe, who finished first time from close range.
It was the France forward’s 23rd league goal, leaving him eight goals clear at the top of the scoring charts.
“Playing at Valencia is always like going to the dentist,” Arbeloa told reporters.
“We knew how difficult the match would be, how demanding they would be. It was a very serious and committed match. I’m happy.
“We can certainly raise our game in terms of brilliance. We have a lot of room for improvement. But a team is built on solidity and commitment. (Thibaut) Courtois didn’t make a single save today. Dedication, commitment, sacrifice. Madrid demonstrated those values once again today,” he said.
Elsewhere on Sunday, Atletico Madrid slipped further adrift in the title race after a 1-0 home loss to Real Betis.
Antony struck in the 28th minute with a fierce effort from the edge of the box, earning Manuel Pellegrini’s side a valuable victory as they bolstered their push for European qualification.
Atletico are a distant third in the table on 45 points, three points ahead of fourth-placed Villarreal, who have two games in hand. Betis sit fifth on 38 points.