Valencia led 1-0 after Hugo Duro’s 66th minute strike but Real rallied late, with Vinicius Junior’s deflected 86th minute effort squaring the game up.
Two minutes later, Real claimed the lead and the win when Vinicius Junior crossed for Karim Benzema to glance in.
“We didn’t win today as a result of our quality, it was down to the teams unbreakable spirit,” Benzema said after the game.
“We kept a cool head and kept going right until the end. My team is quite young but they’re doing very well.
“We must improve defensively because we have to be more aggressive without the ball, we’re going to get it right with this spirit.”
The result means Real remain top of La Liga with 13 points from five games, ahead of champions Atletico Madrid who have 11 points after drawing 0-0 with Athletic Bilbao on Saturday.
Both goal scorers Benzema and Vinicius Junior have been key parts to Real’s strong start to the new season.
The French striker has six goals, while the young Brazilian has netted five times.
“They’re playing very well,” Ancelotti said. “The guys up top did well and combined well with Hazard, even though we had our difficult spells and weren’t fresh in the first half.
“They played a perfect counter-attacking game and in the second half, in control of the game, they demonstrated that they are very dangerous.”
Elsewhere on Monday, Barcelona are up against Granada, with the Catalans in 10th having only played three games.