Soderling, who won in Rotterdam last week, struggled to find a rhythm and had to save two break points in the first set. Llodra had 12 aces and saved a break point in each set before winning his match.
Third-seeded Mikhail Youzhny rallied to beat Gilles Simon 3-6, 6-3, 6-3 in a match that featured eight service breaks and lasted a little under two hours. He next faces another Frenchman, No. 6-seeded Jo-Wilfried Tsonga, in the quarters.
Ljubicic fired 15 aces but could not force a break point against Tursunov, who earned the only break of the match in the second set. Tursunov faces No. 4 Jurgen Melzer of Austria in the quarterfinals.
Cilic advanced after beating Philipp Petzschner of Germany 7-6 (3), 6-3.