Fanning scored 32 off 161 balls at a strike rate of 19.88 as WA went to tea on day two at 6-132 in reply to NSW's 180 at the WACA Ground.
Teenager Teague Wyllie (52no off 129 balls) and Joel Paris (13no) made it safely to tea, with WA still needing another 49 runs to take a first-innings lead.
NSW pace bowler Ben Dwarshuis, in his Shield debut, has been the chief destroyer with figures of 4-32, while Jack Edwards claimed 2-13 off nine overs.
The Warriors started the day at 2-18 and Hilton Cartwright (16 off 56 balls) seemed a tad unlucky to be given out LBW to Jack Edwards (1-5).
Although the ball struck Cartwright on the back leg, it looked as though it was going to sail over the stumps.
But WA received a couple of lucky breaks just before lunch.
Wyllie survived a confident LBW shout from paceman Liam Hatcher.
And next over Fanning was lucky to be given not out after being struck on the pads by spinner Nathan Lyon.
Fanning's strike rate of 19.55 at the lunch break didn't make for pretty reading.
But the 21-year-old's grit on a tricky wicket proved crucial in steadying the ship.
Wyllie's determination also proved vital as the 18-year-old posted his maiden first-class half-century in just his third appearance.
Dwarshuis left WA reeling with two quick wickets late on Monday, and he returned to take the key scalps of Josh Philippe and Aaron Hardie shortly before tea.
NSW's meagre first innings score of 180 would have been far less had it not been for captain Kurtis Patterson, who defied a five-wicket haul from speedster Lance Morris to finish unbeaten on 72.
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