For the first time, six British players have won first-round matches at the Australian Open but Boulter had to work extremely hard to join Jack Draper, Emma Raducanu, Jodie Burrage, Harriet Dart and Jacob Fearnley in round two.
The 22nd seed was on the ropes early in the third set against her 98th-ranked opponent but, with fiancee Alex De Minaur heading from his own victory on Rod Laver Arena to cheer her on, Boulter dug out a 6-4 3-6 7-5 win.
“That was way too stressful for me,” said Boulter, who began her season in great form at the United Cup and headed to Melbourne Park with expectations high.
She welcomed the moment of history, saying: “It’s awesome to have some positivity coming out around British tennis.
“It’s been coming for a long time. It’s just the beginning. I really think these girls and guys have been working so hard and everyone deserves a bit of credit. Obviously it’s a great start for everyone and let’s hope we can keep that going.”
Boulter sensed from cheers she could hear across Melbourne Park that De Minaur had won and his arrival, coupled with enthusiastic support from the crowd, helped her across the line.
“I think I heard his mum’s voice from the crowd,” she said. “That was the first thing I heard before he came. I kind of felt comfortable that he had won and that I could fully relax.
“There is always going to be one per cent of me that’s probably thinking about that but I’m fully focused on what I’m doing and kind of in the zone at the same time.
“Having him come out and support means pretty much everything to me. Having the extra positivity from my bench makes the difference.”
Marino lost to Raducanu at the Billie Jean King Cup Finals in November but looked dangerous in the second set once she got her powerful serve and groundstrokes going.
The 34-year-old was much more settled early on here while Boulter made a nervous start, back-to-back double faults handing over an early break, although that was swiftly retrieved.
The British number one then broke again to lead 4-3 and all appeared reasonably comfortable when she converted her third set point.
But Marino hit a purple patch to begin the second set, breaking the Boulter serve in the second game and the British number one’s frustration grew.
She usually maintains a positive demeanour but here she was smacking her racket against her hand and she could find no way to apply any real pressure to the Marino serve.
At the start of the deciding set, the pressure was all on Boulter and she did well to save a break point in the opening game and then two more at 2-2.
After one point of the next game, De Minaur, who had been watching the contest from an exercise bike while he warmed down, sprinted down the steps to join his partner’s team.
Boulter needed all the support she could get and there was disbelief on her face at some of the shots Marino was making.
But she finally found some traction on return with the Canadian serving at 5-6 and took her second match point when Marino netted.
It was a hugely satisfying win for Boulter, who said: “I felt like it was a mental battle in the end and I managed to do it eventually.
“I’m really pleased to be in the second round, because ultimately these matches for me are the most important ones. Finding a way when someone is swinging free is the difference between the top players and the ones that are ranked slightly lower.”
The 28-year-old next meets Russian Veronika Kudermetova.
