Dart, 25, won 7-6 6-3 and her run in this event could see her break into the world's top 100 for the first time.

"My ranking might not show where my level is, but I've always believed my level has been there," the Briton said.

"I put in the work day in, day out, and finally to be able to put a run like this together, it's not by chance.

"I always have nothing to lose - especially at these events. It's kind of a bonus to be able to play another match in this amazing place. It's quite surreal. I'm enjoying every minute of it."

Dart, who is ranked 122 in the world, will play Australian Open semi-finalist Madison Keys on Tuesday.

Raducanu meanwhile told BBC Sport she has been struggling with a stiff back for the last few days and "was pretty tired".

But the world number 13 says she should be fit to play at the Miami Open from 21 March.

"I think it's just part of not playing and having so much stop start and having five, six days to prepare for matches and then playing at that intensity," she said.

"It was a tough one not being able to serve full out so I was having to work so hard just to hold. I've just got to get stronger.

"I've had it for the last few days, just a product of training hard and probably the last match was pretty intense too and it didn't settle down.

"When you are crossing your fingers to hold serve every time, it's tough. I couldn't really drive up and I was kind of struggling to turn and reach. The margins were so small.

"I should be good for Miami, for sure."

The Briton won four straight games to lead 5-3 in the first set but Martic broke back to force a tie-breaker, which Raducanu won with a superb passing shot.

Martic led 4-2 in the second and although Raducanu levelled it up at 4-4, Martic took it into a decider after claiming her third break of the set.

Raducanu was on the brink of victory after breaking Martic for a second time in the decider to go 5-4 up but Martic again fought back, dropping just two points in the last two games.

The 31-year-old finished with three breaks in the final set to set up a meeting with 28th seed Liudmila Samsonova in the last 16.