Baker defeated fifth-seeded Jerzy Janowicz 4-6, 7-6 (7-5), 6-4. Both players had two breaks but took very different routes there. Janowicz finished off both of his break chances -- one each in the first and third sets -- while Baker had a pair of breaks -- both in the third set -- in 17 break opportunities.
Janowicz pounded out 11 aces but also had 10 double faults in the loss.
Malisse eliminated No. 7-seeded Martin Klizan 7-6 (7-4), 3-6, 6-3 behind a 13-ace attack. Each player had three breaks but Malisse managed the only break of the third set to advance.
Eighth-seeded Thomaz Bellucci beat David Goffin 7-6 (7-5), 6-2 by cashing in all five of his break chances and wild-card entrant Olivier Rochus stopped Albert Ramos 6-2, 5-7, 6-2 behind six breaks in Monday's other matches.
World No. 4 David Ferrer, who beat Rochus in last year's Heineken Open final, is this week's top seed. He is seeking a third consecutive (fourth overall) Auckland title.