By reaching the semis in Rome the Serb also retained hisworld number one ranking and avoided surrendering top spot to Russian Daniil Medvedevfor the second time this year.
Djokovic and Auger-Aliassime were neck and neck until theSerb broke to lead 5-3 but the eighth seed fought back.
It proved only a blip though as Djokovic wrapped up theopening set in style.
The 21-year-old Aliassime was applauded by Djokovic forhis display of endurance in rallies but again fell 5-3 behind, only to draghimself back into the contest again.
Having forced a tiebreak though, Aliassime was no matchfor Djokovic who found another gear when required.
Djokovic will next face Norwegian fifth seed Casper Ruudwho continued his good form on European clay as claimed a hard-fought 7-6 (7),7-5 win against Canada"s Denis Shapovalov.
"He has the lethal serve honestly... It was not easyfor me at all to return. He"s also returning well, moving well. He"s a verycomplete player," Djokovic told reporters.
"I was a set and 5-2, match point, serving for thematch. Credit to him for fighting back. Amazing atmosphere as welltonight."
World number three Alexander Zverev remained on course toclaim his first title of the season after overcoming Cristian Garin to set up asemi-final showdown with Stefanos Tsitsipas, who saw off home favourite JannikSinner.
Zverev, who won the title in Rome in 2017, eased into thelast four with a 7-5, 6-2 win over Garin in the pair"s first meeting since theChilean upset him on home soil en route to winning the ATP 250 event in Munichthree years ago.
Garin, the only unseeded player remaining, had the firstbreak point of the match at 3-2 but Zverev squirmed his way out of it and brokehis 25-year-old opponent to take a 4-3 lead and, after some poor shotselection, closed out a gritty opening set.
Zverev comfortably won the second set after Garin droppedserve in the opening game.
"I think it was a high level match, at times itwasn"t pretty tennis but I got the job done and that"s the most importantthing," said Zverev, who is yet to drop a set in Rome.
Tsitsipas kept his composure in front of a raucous crowdto hold off Sinner for a 7-6 (5), 6-2 victory.
In an entertaining opening set lasting nearly an hour anda half, Tsitsipas raced to a 3-0 lead and Sinner battled back to draw levelbefore the Greek edged it on the tiebreak.
Tsitsipas cruised through the second set and, after astoppage in play at match point when a spectator fell ill, dealt with Sinner"smiscalculated drop shot to triumph.
The 23-year-old beat Zverev in Monte Carlo beforeclinching the title in April before the German avenged his defeat in Madridlast week.
"He"s a player that challenges me when I"m out onthe court," Tsitsipas said of Zverev. "He has a lot of experience onthe tour, much earlier than when I started playing here.
"We have similar game styles but he is one of themost difficult players on the tour."
