The seventh-ranked Nalbandian will next face either Joachim Johansson or Nicolas Mahut at the Royal Tennis Hall.
Second-seeded Mario Ancic of Croatia also advanced, overcoming a slow start to beat Olivier Rochus of Belgium 7-6 (6), 6-2. He will next face either his brother, Christophe Rochus, or Steve Darcis.
Fifth-seeded Rainer Schuettler of Germany easily ousted Chris Guccione of Australia 6-0, 6-3 and will now face Nicolas Lapentti of Ecuador.
Johansson wins, Bjorkman loses at Stockholm
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Isner, Reynolds, Haas win at Legg Mason