Starc (4-56) continued his sizzling start to the season with a devastating hat-trick which ended WA's first innings at 176, a deficit of 94 runs.
Left-arm quick Starc produced a trio of ferocious yorkers which bowled Jason Behrendorff for 20, trapped David Moody lbw and rattled No.11 Simon Mackin's stumps.
He swelled his tally of Shield victims to 14 in three innings at an average of just 12.5.
Smith added an unbeaten 74 to the 76 he scored in the NSW first innings as he helped the Blues to 2-166 - and a lead of 260 - by stumps on day three.
Smith compiled an unbroken third-wicket partnership of 124 with Kurtis Patterson, who finished the day unbeaten on 60.
WA opener Cameron Bancroft supplied the only sustained WA resistance, carrying his bat for their top score of 76, the highest score by a wicketkeeper in Shield cricket this season.
He batted for 286 minutes and survived for 187 balls against a NSW quartet that is widely tipped to comprise Australia's first Test attack.
Starc struck with just his second ball of the day when he had Jonathan Wells caught behind.
Fellow paceman Pat Cummins (2-31) and spinner Nathan Lyon (1-39) each picked up a wicket on day three.