The British No 1 had fought back from a set down to level the match when bad light stopped play on Monday night, and completed the job when the tie resumed on Tuesday afternoon.
Watson prevailed 1-6 6-3 8-6 to reach Wimbledon’s second round for the third time in her career, claiming a fair scalp in dismissing the 32nd seed in the process.
Guernsey-born Watson had struggled for a foothold in the first set against Garcia, slipping behind in alarming fashion.
The world No 64 regained her composure and confidence to steal the second set and tie the match though, with poor light then moving the clash into a second day.
The two players battled through with little between them when play resumed, until Watson edged ahead to serve for the match.
Leading 5-4 and with the tie at her mercy, Watson was unable to complete the job, Garcia breaking back to extend the contest still further.
But the second time 23-year-old Watson had the chance to serve out the match, she did not waste it.
Hantuchova is up next for Watson, the former world number five now stooping as low as 89 in the rankings.
Watson will head into that tie with the 32-year-old Czech in buoyant mood - especially as victory there would most likely set up a clash with 20-time grand slam champion Serena Williams.
And while No 3 seed Andy Murray sauntered through in straight sets against Kazakhstan’s Mikhail Kukushkin, Kyle Edmund’s wait to break into the world’s top 100 goes on after Beverley-born 20-year-old slipped out of Wimbledon, with Alexandr Dolgopolov victorious 7-6 (7/4) 6-1 6-2.
Britain’s world No 101 Edmund was just unable to edge his ranking to double-figures after reaching the second round at the French Open.
He would certainly have achieved that big goal by reaching the second round at SW19, but was unable to overcome his Ukrainian opponent.
Dolgopolov dumped Rafael Nadal out of this year’s Queen’s Club, and continued that fine form by easing past Edmund without issue.
Elsewhere, Brydan Klein became the second British player to bow out on day two as he lost on Court 18 to Italian 25th seed Andreas Seppi.
Australian-born Klein, who has been competing as a Briton since 2003, was resoundingly outplayed by Seppi who coasted to a 6-3 6-2 6-2 victory.
Laura Robson was unable to put ring-rustiness from her 17-month wrist injury absence to bed against Evgeniya Rodina, losing out in straight sets 6-4 6-4.
The former British No 1 battled with service action shortcomings throughout, and slipped of Wimbledon in just the second match of her long-awaited comeback.