Duckworth, who made the second round at last month's Australian Open, pushed second-seeded Norwegian Casper Ruud, claiming the second set but ultimately falling 7-5 4-6 6-2.
Ruud had to work hard in the first set, saving all three break points he faced, before breaking Duckworth's serve once.
The Australian rallied in the second set to send the match to a decider, but ran out of steam as Ruud closed it out 6-2 in the third.
Vukic, ranked No.67 in the world, fought hard but lost 6-3 6-3 to in-form American Ben Shelton, who made the semi-finals at Melbourne Park.
Aleksandar Vukic (pic) put up a strong fight but lost in straight sets to Ben Shelton. (Lukas Coch/AAP PHOTOS)
Shelton was untouchable on serve on Tuesday (Wednesday AEDT), not facing a break point all match, while Vukic was broken three times.
Despite the loss, it has been an incredible month for Vukic who beat American 22nd seed Sebastian Korda on his way to the third round of the Australian Open.
Vukic threatened to go even deeper in the grand slam by winning the first two sets against 15th seed Jack Draper, but the Brit fought back to clinch the match in a fifth-set tiebreak.
It was a bittersweet loss for Vukic, who then made his Davis Cup debut for Australia against Sweden in Stockholm, where he beat tennis legend Bjorn Borg's son Leo in straight sets.
Vukic had been hoping to follow the successful start in Texas by fellow Aussie Rinky Hijikata, who scored an impressive 7-5 6-3 win over French veteran Adrian Mannarino.
Meanwhile, top-seed Tommy Paul, who made the Australian Open quarter-finals, was pushed all the way by fellow American Jenson Brooksby in Dallas before prevailing 6-7 (8-6) 6-3 6-4.
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