The 2015 French Open champion, who has yet to drop a set this week, may have won in three but it was tougher than it looked. The unpredictable Dolgopolov, a former top-20 player, gave him a run for his money.
"He pushed me, he pressed me and I had to stay concentrated," said Wawrinka. "It was a big game and the level was extremely high.
"I had to keep pushing back. I served well and that helped so I am satisfied," said the Swiss, who fired 16 aces compared to the Ukrainian's six.
Wawrinka and Dolgopolov broke each other once early in the first set and both players aggressively looked for quick winners with their rallies lasting an average of 2.8 shots.
But the 32-year-old Wawrinka, aiming to become only the third man in the professional era to win three or more slams after turning 30, squeezed in another break to snatch the first set with a fierce backhand down the line.
The pair traded blows in a finely balanced second set before taking it into a tiebreak, with Wawrinka again emerging victorious. He sealed the second set with an ace.
It was a similar story in the third set with both players pummelling each other until Wawrinka broke Dolgopolov a second time to clinch victory and deny the world number 89 his first third round spot in Paris since 2011.
Mercurial Fognini could be equally tricky and Wawrinka said he was not looking forward to playing him.
"He is unpredictable like Dolgopolov," said the Swiss, one of 30 men over the age of 30 to have made the second round of the claycourt major -- a professional era record. "It will be a dangerous match."
Asked if he was looking forward to the third round encounter, Wawrinka said: "Not really. I don't know anyone who likes to play that kind of player."
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
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