Among 102 players vying for 10 spots, Jones finished the 36-hole qualifier in Dallas tied for fifth at 5 under par following rounds of 66 at Bent Tree Country Club and 70 at Northwood Club.
The 39-year-old was the only Australian to advance in Texas and narrowly avoided a playoff, with three players at 4 under forced into extra holes to decided the last two spots.
Countrymen Nick Flanagan and Harrison Endycott finished at even par and 1 over respectively while Rhein Gibson withdrew following a morning round of 70 at Bent Tree.
In three previous appearances at the US Open - 2009, 2014 and 2018 - Jones has never made the cut.
A host of other Australians will compete across 11 more sectional qualifiers including events in Japan on May 27 and England and Canada on June 3.
A further eight US qualifiers will also be held on June 3.
The 119th US Open gets underway at Pebble Beach on June 13.
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