Thiem, who before this week had never won a match in five attempts in Canada, had his hands full against 14th-seeded Cilic but did well to save all nine break points he faced while relying on a steady stream of groundstroke winners.
The Austrian, who arrived in Montreal fresh off a claycourt title in Kitzbuhel where he was the top seed, said his triumph on home soil helped ease the transition to hardcourt tennis.
Up next for Thiem will be Russian eighth seed Daniil Medvedev, a 6-3 6-3 winner over Chile's Cristian Garin.
In other action, sixth-seeded Russian Karen Khachanov rallied to beat 19-year-old Canadian birthday boy Felix Auger-Aliassime 6-7(7) 7-5 6-3 to reach the quarter-finals.
Third seed Alexander Zverev of Germany will face Khachanov in the quarters after a 7-5 5-7 7-6(5) win over Georgia's Nikoloz Basilashvili.
Top seed and defending champion Rafa Nadal will kick off the evening session against Argentine Guido Pella, an opponent he has beaten in each of their three career meetings.
On the women’s side, Karolina Pliskova beat Estonian Anett Kontaveit 6-3 7-5 to set up a Rogers Cup quarter-final showdown with Canadian Bianca Andreescu and keep alive her hopes of reclaiming the world number one ranking.
Ukrainian sixth seed Elina Svitolina, who won here in 2017, also reached the quarter-finals with a 6-2 6-4 win over Swiss Belinda Bencic to set up a meeting with Sofia Kenin. American Kenin, who stunned world number one Ash Barty in the second round, reached the last eight with a 6-2 6-2 win over Ukrainian teenager Dayana Yastremska.