Henriques was dismissed for 95 late on day two on at the WACA to fall just short of his 14th first-class century.
But the 37-year-old has put NSW in a position to cause a boilover, which would continue their Blues' resurgence in the Shield.
NSW went to stumps at 7-244, trailing WA by just 12 after bowling the hosts out for 256 on Saturday.
Spinner Chris Green (17) and veteran pacer Jackson Bird (11) will resume on Monday trying to put the Blues into the lead.
NSW started their innings on Sunday but fell into early trouble at 3-30 as quick Joel Paris and spinner Corey Rocchiccioli ran through the Blues' top-order.
But Henriques was able to dig in, forming important partnerships with Ollie Davies (21) and in-form allrounder Jack Edwards (34).
Paris was the pick of WA's bowlers with 3-45 from 22 overs, while Rocchiccioli sent down 32 overs in a day for 3-96.
WA, who have won the last two Shield finals, sit second after winning three games before the break for the BBL.
NSW are trying to claim an unlikely double against WA this season.
In November, the Blues snapped their longest winless Shield run when they upset WA at the SCG to secure their first victory in 21 months.
NSW added another victory to their tally after that, downing ladder-leaders Tasmania to regain confidence.
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