Federer, the No. 1 seed and defending champion, dispatched Thiemo De Bakker 6-3, 6-4 in an efficient 62 minutes. Federer won nearly three-quarters of the points on serve, facing one break point. He had a break in each set in the win.
Del Potro, the second seed, ousted Ernests Gulbis 7-6 (7-5), 6-3, using the lone break of the match to take the second set. Del Potro saved the two breaks points he faced.
Jarkko Nieminen got by Matthias Bachinger 6-3, 5-7, 6-3 and Martin Klizan defeated Igor Sijsling 6-2, 6-4.
De Bakker and Sijsling were the last two Dutch players in the draw.
Federer draws Julien Benneteau Friday while Klizan plays No. 5-seed Gilles Simon in the other top-half quarterfinal. Del Potro goes against Nieminen and Baghdatis faced Grigor Dimitrov in the other matches Friday.