The Knights were poised for a reasonable advantage when they bowled the Cobras out for 294 and then reached 264 for six in reply, but Paterson pulled off a crucial run-out and then grabbed a brace of wickets to level the game up.
With Muller bowling Duanne Olivier off what proved to be the final ball of the day, the Knights were dismissed for 304 to set up a second-innings shootout over the last two days.
Muller and Paterson were also responsible for a crucial 10th-wicket partnership of 43 that carried the Cobras to a more competitive total.
The visitors resumed on 251 for nine, and set the tone for a positive day as Muller scored 15 and Paterson 27 not out before Shadley van Schalkwyk (3/59) cleaned up the former batsman to bring the innings to a close.
Muller then struck early to remove the dangerous Reeza Hendricks, while Beuran Hendricks accounted for Tumelo Bodibe and Gihahn Cloete (47).
With Paterson dismissing Rudi Second and Muller grabbing a second scalp in Obus Pienaar, the Knights were in trouble at 117 for five but Pite van Biljon’s 55 pulled them back into the game before Werner Coetsee (74) and Van Schalkwyk (62) edged them in front.
Coetsee and Van Schalkwyk had added 82 for the seventh wicket when Paterson ran out the Knights skipper, and five overs later the Cobras paceman trapped Van Schalkwyk lbw to open up the tail.
Another blow for Paterson gave him figures of 3 for 53, while Muller had 3 for 58 after the Olivier dismissal.