Novak improved to 3-0 against British qualifier Aljaz Bedene in their H2H series on Tuesday at the Internazionali BNL d’Italia in Rome.
Nole goes on to play Feliciano Lopez (ESP, H2H 8-1) in the last 16 on Thursday.
Next up for the two-time former champion is no.13 seed Pablo Carreno Busta (ESP).
Novak and Viktor saved one match point en-route to a 5-7, 6-1, 11-9 victory over Pierre-Hugues Herbert and Nicolas Mahut. They face Klaase/Ram in quarter-finals.
The defending champion goes on to face no.31 seed Juan Martin del Potro for a place in the ATP Masters 1000 event last 16.
Novak advanced past the Argentine 4-6, 6-4, 6-4 in two hours and 38 minutes to move to 12-4 in their ATP Head2Head series.
Wildcard Denis Istomin prevailed in five grinding sets after four hours and 48 minutes of play at Rod Laver Arena on Thursday.
Novak eased past Argentine Horacio Zeballos 6-3, 6-4 in 72 minutes on Wednesday to advance into the last eight in Doha.
The reigning Paris Masters champion beat world no.34 Gilles Muller 6-3, 6-4 and next faces no.14 seed Grigor Dimitrov (Thursday).
Nole began his title quest at the ATP Masters 1000 event with a comfortable 6-3, 6-3 victory over world no. 50 Fabio Fognini.