Top seed Djokovic, who needs a Roland Garros title to become just the eighth man to complete a career Grand Slam, will tackle defending champion Rafael Nadal for a place in Sunday's final.
"Tommy is a very dangerous opponent with lots of quality, plenty of experience and is very aggressive," said Djokovic.
He will go into Friday's semi-final having defeated Nadal in the final of Monte Carlo on clay in April.
"I will have to raise my game for the next match. Nadal is in great form but the win in Monte Carlo has given me great confidence. I will be positive."
It was a match too far for the 35-year-old Haas who was bidding to become the oldest semi-finalist at a major since Andre Agassi at the 2005 US Open and second oldest in Paris.
Djokovic has vowed to win the tournament in honour of his childhood coach, Jelena Gencic, who passed away at the weekend, and he raced away in the first set.
The 26-year-old, the runner-up to seven-time champion Nadal last year, reeled off breaks in the seventh and ninth games that gave him the first set in which Haas won just a single point on the Serb's serve.
But Haas held on for a second set tie-break, even nipping ahead for 4/2 before Djokovic reeled off five of the next six points to take it courtesy of a trademark, deep, booming forehand.
The German, a former world number two whose career has been decimated by a series of injuries, slipped 2-1 down in the third before he carved out and converted his first break point of the quarter-final to level at 2-2.
Back came Djokovic, breaking again for a 4-3 lead before Haas saved a match point in the ninth game.
He refused to buckle, breaking Djokovic a further time as he served for the match to level at 5-5.
But the Serb wasn't to be denied taking victory on his second match point.
Haas was left with the slender consolation of having reached a Roland Garros quarter-final for the first time at the 12th attempt, a year after having to qualify for the tournament.
He also went away with a slice of history having needed a record-setting 13 match points to beat John Isner of the United States in the third round.
French Open quarter-final results (x denotes seeded player):
Men:
Quarter-finals:
Novak Djokovic (SRB x1) bt Tommy Haas (GER x12) 6-3, 7-6 (7/5), 7-5
Rafael Nadal (ESP x3) bt Stanislas Wawrinka (SUI x9) 6-2, 6-3, 6-1
Women:
Quarter-finals:
Victoria Azarenka (BLR x3) bt Maria Kirilenko (RUS x12) 7-6 (7/3), 6-2
Maria Sharapova (RUS x2) bt Jelena Jankovic (SRBx18) 0-6, 6-4, 6-3