The Spanish world number two and her battling Italian opponent, ranked 65 places below, entertained the Centre Court with intense rallies of relentless ferocity.
It was the confidence and enormous serve of last year's runner-up Muguruza that got the better of Giorgi - but not before the 24-year-old Italian had overcome bouts of inconsistency to force a forehand error and grab the second set.
As she has done for most of the past 19 British summers, Venus Williams took a large, languid stride into the second round.
The oldest woman in the main singles draw, five-times champion Williams was at times sublime as she beat Croatian Donna Vekic 7-6 (7-3), 6-4 on a sunny Court One.
And in the tournament's first big surprise, former top-ranked Ana Ivanovic was beaten 6-2, 7-5 by Ekaterina Alexandrova, a Russian qualifier ranked 223rd in the world and making her Grand Slam debut.
The Serb blamed a wrist injury for a surprise defeat to a player who had never played in a grand slam prior to this match.
Tomic overcame two more rain delays and Fernando Verdasco's ferocious firepower to prevail 4-6, 6-3, 6-3, 3-6, 6-4 in a tense first-round battle continuing on from Tuesday.
The 19th seed joins fellow Australians Nick Kyrgios, John Millman, Daria Gavrilova and Samantha Stosur in the second round, but the bleak weather in London left Wimbledon debutant Matt Barton on tenterhooks for a second night running.
Barton was locked at two sets apiece and 3-3 in the decider when his titanic first-round tussle with fellow qualifier Albano Olivetti was abandoned on Wednesday night.
Samantha Stosur did not even set foot on court, with the 14th seed's second-round clash with former finalist Sabine Lisicki wiped entirely from the third-day schedule.
But Tomic made the startling confession that he would have preferred not to return to court after a second rain stoppage and instead gone to bed leading Verdasco 5-3 in the fifth set.
"I was leaning on hopefully playing tomorrow and then not having to play (my) second (match) if I had have won," he said.
"Now I have to play tomorrow."
The 19th seed will return on Thursday to face Moldovan qualifier Radu Albot for a likely crack at 14th seed Roberto Bautista-Agut.