Agassi broke the unseeded Dane's serve in the third game of the match and was never threatened after that in the opening set. He repeated the feat at the same stage of the second set and coasted to victory from there.
The American next meets Frenchman Paul-Henri Mathieu, who advanced with a 7-6, 6-4 win over Adrian Garcia.
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In other matches, Gilles Muller of Luxembourg scored a 7-5, 5-7, 6-2 win over American Jan-Michael Gambill, and Switzerland's Michel Kratochvil also advanced with a 7-6, 7-6 victory over eighth-seeded Russian Dmitry Tursinov.
Muller and Kratochvil will face each other in the last eight.