After rain ruined most of day one, 14 wickets fell on Sunday in Perth to put the visitors narrowly in front.
Resuming on 3-35, NSW were dismissed for 170 and then had WA floundering at 7-116.
Bancroft mirrored NSW opener Sam Konstas (four) as Ashes top order hopefuls who did not advance their causes in their first innings at the WACA ground.
The WA opener had made 10 when a superb delivery from opening bowler Ryan Hadley appeared to have him caught behind.
But replays suggested the noise might not have been an edge, but the ball glancing the off bail on the way through to wicketkeeper Matthew Gilkes.
The bail wobbled, but stayed put - meaning Bancroft would have been not out had he not nicked the ball.
In better news for Test hopefuls, WA all-rounder Cameron Green took a wicket in four overs on Sunday - his first bowling at first-class level since his back surgery late last year.
Will Salzmann top scored for NSW with 43 and Gilkes made 37 for NSW, while Ashton Agar took three wickets late in the innings.
Agar (18) and Matthew Kelly (20) came together with WA struggling at 7-84, surviving to stumps.
Hilton Cartwright made 34, while Hadley had taken 3-29 from 12 overs.