The Swiss was joined in the last eight by Andy Murray, who coped well with the blustery conditions in the Magic Box stadium to beat Spanish 16th seed Tommy Robredo 7-5, 6-1.
Federer, knocked out by Blake at last year's Beijing Olympics, laid down a marker in the opening game, breaking the American's serve with a crashing backhand return.
The 13-times grand slam winner, who has yet to win a title this year, wrapped up victory with a fifth ace on his first match point. He will play the winner of the match later on Thursday between sixth seed Andy Roddick and Nikolay Davydenko.
A single break of the Robredo serve in the 11th game of a tight first set and three more in the second were enough to seal a comfortable win for Murray and the Briton converted his first match point with a backhand return down the line.
He will play Juan Martin Del Potro on Friday after the Argentine battled past 11th-seeded Swiss Stanislas Wawrinka 4-6, 6-4, 6-4 on Thursday.
Jankovic advances
In the women’s event, world number four Jelena Jankovic swept into the last eight with a 6-2, 6-2 victory over Russian Elena Vesnina on Thursday.
Jankovic stuttered when serving for the match at 5-1 in the second set but broke Vesnina for the sixth time in the next game when the Russian failed to deal with a thumping backhand.
Ukrainian Alona Bondarenko entered quarterfinal beating Russian Anna Chakvetadze 6-0, 2-6, 6-3.
Sania-Chuang through
India’s Sania Mirza and Chia-Jung Chuang of Chinese Taipei (Taiwan) upset second seed Spaniards Anabel Medina Garrigues and Virginia Ruano Pascual 7-6(4), 4-6, 10-7 to enter the doubles quarterfinal.
Somdev crashes out
In Zagreb, India’s Somdev Devvarman went down fighting to Brazilian Ricardo Hocevar in the second round of the $50,000 Association of Tennis Professionals (ATP) challenger.
Somdev, who is playing his first clay tournament of the season, lost 4-6, 6-7(4) on Wednesday. Hocevar in the quarterfinal plays Serbian Boris Pashanski, who beat German Daniel Brands 7-5, 7-6(3).
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