Uruguayan Valverde showed composure to calmly beat a defender with clever footwork on the edge of the area before picking his spot in the bottom corner of the net in the 80th minute.
The 14-time winners gave an underwhelming performance and until Valverde's goal had only managed one shot on target, while Leipzig had created plenty of openings but were not clinical enough in the area.
Real wrapped up the victory with a goal in added time from substitute Asensio, the Spaniard slotting into the net after a layoff from Toni Kroos (32).
Real coach Ancelotti praised Valverde for opening up a cagey game and said he has been urging the Uruguayan to take more shots.
"What surprised me is how little he scores, he only scored one goal last season. I told him that he has a wand of a foot, he has an incredible shot, and that he has to score at least 10 goals this season," said the Real coach.
He also admitted that his side had been far from their best.
"It was not a fantastic performance from us, but we wanted to limit their counterattacks and that's why we didn't play with a very high line or press too high up the pitch," he said.
"We wanted to win so it was very important to be vigilant defensively. But when their energy dropped we pushed on and in the end, deserved the victory."
The Spanish side lead Group F with six points after two games, while Leipzig are bottom with no points. Ancelotti's side host second-placed Shakhtar Donetsk in their next game on October 5th, when Leipzig host Celtic.
In their first Champions League match under new coach Marco Rose, Leipzig took the game to Real and were comfortably the better side in the first half, with forward Christopher Nkunku (24) causing the hosts plenty of problems.
Real offered little going forward but felt they should have had a penalty when Luka Modric (37) was smothered by Xaver Schlager (24) shortly before halftime.
The same script was followed for much of the second half until Valverde, who had scored a sensational goal against Real Mallorca at the weekend with a run from his own half, provided the breakthrough moment.
"It was a tremendous goal, we have to make the most of him because he is in brilliant form," said Real defender Nacho (32) of Valverde.
"It was a really hard-fought game, we were a bit out of sync but we spoke about it at halftime and we have a lot of power and are always capable of scoring," he added.
Real face cross-town rivals Atletico in the Madrid derby this weekend.
