Dodig lost the first set but used 19 aces to bounce back and hang a tense 5-7, 6-4, 7-6 (10-8) defeat on Tomic at The Racquet Club of Memphis on the tourney's opening day.
Tomic proved tough down the stretch, gaining two match points in the final-set tiebreaker.
But the Croatian responded by scoring three points to claim the match.
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