Playing the day after his grandfather died, the top-ranked Djokovic looked distracted at times against Haase.
He missed a first chance to serve out for the match at 5-1 before breaking the unseeded Dutchman for the seventh time to seal victory.
The win kept Djokovic on course for a final against seven-time defending champion Rafael Nadal, who overcame a slight blip in the first set before beating Stanislas Wawrinka 7-5, 6-4 for his 40th consecutive win at Monte Carlo.
Fourth-seeded Jo-Wilfried Tsonga was upset 7-5, 6-4 by ninth-seeded Gilles Simon in an all-French match.
Djokovic had considered withdrawing before his third-round match on Thursday, which came only a few hours after he’d received the bad news.
“Yeah, I did. But I’m a professional and life goes on,” he said. “I know that I cannot change anything now. Obviously, it’s what life gives you and takes (from) you. It’s a normal circle of life. I was very close to him, so it was a big loss for me.”
Because of his tennis commitments, Djokovic will be unable to make the funeral back home in Serbia.
“No, it’s not possible. It’s a very sensitive thing to talk about really,” he said. “Every religion has a different way of proceeding, the funerals, life itself.”
Djokovic lost a total of 16 points on his usually rock-solid first serve, and his play was sometimes erratic.
“It’s tough to be able to play tennis after the way I felt and the way I still feel,” Djokovic said. “I remember him as a great man, and I know he’s been supporting me and still from the heavens now.”
Djokovic next plays sixth-seeded Tomas Berdych, who took advantage of a wayward performance from Andy Murray to win 6-7 (4), 6-2, 6-3.