World number one Roger Federer beat Croatia's Ivo Karlovic 7-6, 6-3 in the Rome Masters on Thursday to book a quarter-final against Czech Radek Stepanek.
Earlier, Australian Open champion Novak Djokovic edged past Russia's Igor Andreev 6-3, 3-6, 6-3 in his third round match and will face Spain's Nicolas Almagro in the last eight.
Top seed Federer's fluid tennis met stubborn resistance from Karlovic in the first set. The Croat, aided by some brutal serves, saved four break points in the eighth game and a set point in the 12th before losing the tiebreak.
Federer then drilled a forehand on to the line to clinch the third of three break points in the fifth game of the second and broke again in the final game of the set to cruise home.
Third seed Djokovic had to work much harder against Andreev.
After an early exchange of breaks, the 20-year-old Serb took Andreev's serve in the fourth game with impressive returns and wrapped up the set with a beautifully executed serve-and-volley.
But the Russian had no intention of lying down in their third round match and pulled back into contention by taking the second set having broken in the fourth game.
Djokovic looked rattled for a spell and came close to losing his serve again three times before regaining his composure to break in the second game of the final set.
Serbia's world number three had to dig himself out of more trouble in the seventh game of the decider before serving out the match.
Stepanek set up a match against Federer by ending Peruvian qualifier Luis Horna's impressive run with a 6-4, 1-6, 6-3 win.
Almagro, who knocked out Argentine seventh seed David Nalbandian in the second round, went straight into the last eight after Chilean Fernando Gonzalez, last year's finalist, pulled out of their match with a leg injury.
Juan Carlos Ferrero, the 2001 champion, meets Switzerland's Stanislas Wawrinka later on Thursday in their third round match after halting second-seeded Spaniard Rafael Nadal's bid for a fourth straight Rome title on Wednesday.
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