Djokovic has won 20 of his 26 meetings with Wawrinka but the Swiss won their two encounters in Grand Slam finals - the 2015 French Open and 2016 US OpenNovak Djokovic eased past old rival Stan Wawrinka to reach the quarter-finals of the Italian Open.
The pair have met twice in Grand Slam finals, Wawrinka winning on both occasions, but in Rome world number one Djokovic won comfortably, 6-2 6-2.
Wawrinka, 37, now ranked 361st in the world, is making his own comeback after a year out with a foot injury.
He struggled physically and made a series of errors as Djokovic controlled with early breaks in either set.
Djokovic will play eighth seed Felix Auger-Aliassime in the last eight of the clay-court event after the Canadian beat American Marcus Giron 6-3 6-2.
Serb Djokovic is chasing a sixth title in Rome but his first of the year as he builds towards the French Open later this month.
Wawrinka's wins in the previous two rounds were his first since making his comeback in March.
Elsewhere, fourth seed Stefanos Tsitsipas recovered from losing the first set to beat Russian Karen Khachanov 4-6 6-0 6-3.
Second seed Alexander Zverev beat Australian Alex de Minaur 6-3 7-6 (7-5) and Italian 10th seed Jannick Sinner progressed in his home event by seeing off Filip Krajinovic 6-2 7-6 (8-6).
Norwegian fifth seed Casper Rudd beat American Jenson Brooksby 6-3 6-4 while unseeded Chilean Cristian Garin overcame Marin Cilic in three sets.
Rafael Nadal, who could meet Djokovic in the semi-finals, faces Denis Shapovalov later.
