Connolly's polished 70 and fifties from Hilton Cartwright and Jayden Goodwin led WA's final-day resistance in the rain-marred day-nighter at Adelaide Oval.
After day one was washed out, WA were bowled out for 188 and SA replied with 333, with Nathan McSweeney top-scoring with 68. The visitors posted 6-324 in their second innings. Â
WA started Tuesday's final day 2-85, trailing by 60 runs, with SA hoping to engineer a victory push.
But Goodwin followed his first-innings half-century with 55 in another knock of substance, and Cartwright made 64 to defy the South Australians.
The pair combined for a 105-run stand for the third wicket, soaking up more than 40 overs from SA's bowlers.
Hanno Jacobs (1-75) broke the partnership when he bowled Goodwin, ending his 156-ball knock.
Cartwright departed only 10 runs later, launching at a full, wide delivery from Henry Thornton (3-77) but edging to Jake Lehmann at point.
WA were 4-185 but again steadied with Connolly and Aaron Hardie (38) featuring in a 101-run partnership.
But the duo were dismissed in a three-over span as Thornton struck at dusk.
Connolly, a match-winner for Australia in the Adelaide ODI against India last month with an unbeaten 61, hit 11 fours from 135 balls but edged a Thornton cutter.
The SA paceman bowled Hardie in his next over, leaving WA 6-301 as the game drifted through the final session.
Joel Curtis (15) and Corey Rocchiccioli (five) were not out when the draw was called with an hour remaining.
SA sit with one win from five games in their title defence, the same as fellow strugglers WA.
Pacesetters Victoria and Queensland are a dozen points clear with one round remaining before the Christmas break.
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