“The ball is so far out, this is embarrassing, you’re embarrassing yourself. You should be embarrassed,” Dart told official Kelly Rask.

Their heated discussion continued into the change of ends, with Dart offering a £50,000 bet that the ball in question was out.

After asking to speak to the tournament referee, Dart then accused Rask of “threatening” her with a code violation.

An unperturbed Boulter proceeded to serve out the set at the first opportunity to force the decider.

In it, she broke early on and looked to be taking control, only for Dart bring the set back on serve in a drawn-out sixth game, doing so on her fifth break point.

But Boulter soon broke again and served out the win on her third match point.

Earlier, British number five Heather Watson progressed to the second round with a 4-6 6-0 6-4 rain-disrupted win over American Kayla Day.

Watson will next face sixth seed Karolina Pliskova of the Czech Republic.

Elsewhere, British duo Lily Miyazaki and Emily Appleton were both beaten in the first round.

Miyazaki lost 6-4 7-5 to Czech player Linda Fruhvirtova while Australian Kimberly Birrell defeated Appleton 6-3 7-5.

Fellow Briton Emma Raducanu will begin her Nottingham campaign on Tuesday against Japan’s Ena Shibahara, while top seed and world number 10 Ons Jabeur opens against Colombia’s Camila Osorio.