NSW went to stumps on the second day of the four-day match at 230 for six, still 46 runs behind Tasmania's first innings total of 276.
Bevan, whose leg-spin was once an integral part of Australia's One-day attack, has hardly bowled since he turned 30, mainly due to a shoulder injury.
But the 34-year-old former NSW batsman has started bowling again this year, first with Leicestershire in English County cricket and now with his new state team Tasmania.
He bowled Matthew Phelps for 67 and followed up with Jason Krejza's wicket to finish with 2-19 from seven overs.
Bevan's late incursion put first innings points in the balance after NSW looked to be cruising at 188 for four after Phelps and Dominic Thornely (70) lifted the home team out of trouble at 61 for three.
Thornley is challenging Bevan for the honours of leading Sheffield Shield scorer and has taken his season tally to 428 runs, second only to Bevan's 517.
At the close Brad Haddin was 29 not out with Matthew Nicholson on seven.