Swiatek survives error-filled start to reach US Open second round
Swiatek, who counts the 2022 US Open among her five Grand Slam titles, converted three of six break-point chances but also racked up 41 unforced errors en route to securing the victory in one hour and 52 minutes at Arthur Ashe Stadium.
The top-seeded Pole built a 4-0 double break lead and looked poised to run away with an easy win but Rakhimova consolidated a break to get within a game before Swiatek went on to seal the first set with her third love hold of the match.
Swiatek consolidated an early break with another love hold for a 3-1 lead in the second set but suddenly started showing signs of frustration as her shots were off target and Rakhimova refused to back down from the challenge.
Swiatek had a chance to serve out the match but Rakhimova broke to get to 5-5 as the second set went to a tiebreak where the Pole saved three set points before sneaking through to the second round.
The reigning French Open champion will next face either Australian Daria Saville or Japan's Ena Shibahara.