Evans toppled seventh seed Marin Cilic on Wednesday and can now add Tomic to his growing list of scalps after beating the local favourite 7-5 7-6 (7/2) 7-6 (7/3).
The British number three has also reached his first-ever fourth round at a grand slam and he will now face France’s 12th seed Jo-Wilfried Tsonga for a place in the quarter-finals.
Evans’ progress represents the first time Britain has had two players in the last 16 of the Australian Open singles since Tim Henman and Greg Rusedski made it in 2001.
An emotional Evans could barely hold back the tears when the final point was won, looking up to the sky before punching the air with relief.
The contest was not without controversy, particularly when a cramping Evans prompted a 10-minute delay in play at the end of the third set due to spitting rain.
The 26-year-old, however, overcame his physical discomfort as well as a hostile Australian crowd to ensure his remarkable run in Melbourne continued.
“I should say thank you to the crowd,” Evans said on court afterwards.
“It was a great atmosphere and made the match much better, but it was tough. Bernie was difficult, he’s unorthodox, he plays aggressively and sometimes slows it down. I’m happy to come through, they were three tight sets.”
Earlier in the day, Andy Murray beat Sam Querrey 6-4 6-2 6-4 to book a fourth round encounter with Germany’s Mischa Zverev tomorrow.
“I thought I did pretty good today,” Murray said. “The start of the match was hard. Sam came out serving big.
“He was really going for his shots. The end of that first set was important. He had a breakpoint at 4-3. When I saved that and broke the next game, momentum was with me.”
Elsewhere in the men’s draw yesterday, 17th seed Roger Federer beat Tomas Berdych 6-2, 6-4, 6-4, Stan Wawrinka defeated Viktor Troicki 3-6, 6-2, 6-2, 7-6, Jo-Wilfried Tsonga got the better of Jack Sock 7-6, 7-5, 6-7, 6-3, Kei Nishikori beat Lukas Lacko 6-4, 6-4, 6-4, Mischa Zverev saw off Malek Jaziri 6-1, 4-6, 6-3, 6-0 and Andreas Seppi defeated Steve Darcis 4-6, 6-4, 7-6, 7-6.