Gael Monfils produced the comeback of the day to beat Kei Nishikori in three sets while Canada's Denis Shapovalov enjoyed the biggest win of his young career by defeating hard-hitting Argentine Juan Martin del Potro 6-3 7-6(4).
A day after celebrating his 36th birthday, Federer played the aggressive game that has propelled him to five titles, including two grand slams, this year, attacking the net and rocketing second serves.
Polansky never looked comfortable after he double faulted twice in his first service game and had difficulty handling Federer's pinpoint serves.
Federer, who has lost only two of 34 matches this year, will next play Spain's David Ferrer who prevailed in a three-setter against American Jack Sock 7-6(7) 3-6 6-1.
Rafa Nadal enjoyed an easy rout of Croatia's Borna Coric as he raced through the first set in just 29 minutes and did not face a break point until the 13th game.
"At the beginning of the match there were great points. I think I started playing so well in the first set and in general, I played a great match" Nadal told reporters of the 6-1 6-2 win.
"Last time that I played against him I lost, last year in Cincinnati. It was not an easy round for me."
Nadal will next face the 18-year-old Shapovalov who pumped his fists and rose his arms in triumph after dispatching the 2009 U.S. Open champion, who struggled with the accuracy of his serve during big moments in the match.
A Del Potro double fault put Shapovalov up a break at 6-5 in the second set, but nerves appeared to get to the tournament wildcard, who needed a tie-break to prevail.
Monfils, however, fended off four match points to beat Japanese world number nine Nishikori in a three-set thriller 6-7(4) 7-5 7-6(6).
The 27-year-old Nishikori had two chances to serve out the match and led 6-2 in the decisive tiebreak, before Monfils won six successive points to complete a superb fightback.
He will face Spaniard Roberto Bautista Agut in the third round.
Fourth seed Alexander Zverez and seventh seed Grigor Dimitrov each needed three sets to advance while ninth seed David Goffin was upset by South Korean Hyeon Chung 7-5 6-3.
Sixth seed Milos Raonic was also upset by Adrian Mannarino 6-4 6-4 while American Sam Querrey beat France's Jo-Wilfried Tsonga 6-1 3-6 6-4.
(Reporting by Rory Carroll; Editing by Toby Davis/Greg Stutchbury)
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