Moments before the end of this wild encounter between Britain’s two highest-ranked women, Harriet Dart covered her eyes and started to wipe away tears. At 6-2 down in the final set tie-break, she was done. We knew it. She knew it. And what made it really sting? It was her rival Katie Boulter, with whom she has a relationship that makes the Arctic in winter look warm, on the other side of the net.

At this stage Dart’s nerves were so apparent they could have been displayed next to her sponsor Asics’ logo. But this three-hour epic – part tennis match, part psychodrama – had one final twist.

First Boulter hit a sloppy backhand low into the net. Then she sent a wild forehand long. Two more untamed groundstrokes then went into the tramlines. In barely a minute the score was back to 6-6 and Dart was alive again. Soon after 7-7 became 8-8, but when Boulter splayed two more gunslinger forehands long it suddenly was over. Dart had won eight of the last 10 points and taken a 4-6, 6-1, 7-6 (10-8) victory.

It was not a match of the highest quality, to put it mildly. Boulter hit a staggering 75 unforced errors, along with 39 winners. While Dart hit 35 unforced errors to 17 winners. But, my, it was compelling. No wonder No 1 Court lapped it up.

“I wear my emotions on my sleeve so you see everything how I’m thinking, unfortunately,” admitted Dart. “My head-to-head is absolutely woeful against her so I wasn’t expecting too much. And even though I was down in that tie-break I just thought: ‘Give it everything, no regrets.’”

Boulter, meanwhile, insisted that she had not seen Dart’s tears – and so they hadn’t affected her play. “I think she kind of just relaxed a little bit,” she said. “She was 6-2 down. She’s got nothing to lose. I think I played into her strengths at that point as well, thinking back on it.

“We all go to the office sometimes and don’t have good days. That was just me today.”

Dart’s victory means that she joins her two compatriots, Emma ­Raducanu and Sonay Kartal, in the third round, where she will play China’s Wang Xinyu. The last time three British women made the last 32 at Wimbledon, Frankie Goes to Hollywood topped the charts with a song about Two Tribes going to war. It proved an apt description for what played out over three hours.

This was a match suffused with nerves and needle. In the last year Dart has accused Boulter of being “unprofessional” in her celebration after winning one match – and offered to bet the umpire £50,000 that she was right about a disputed line call during another loss.

Dart did not want just victory here. She also wanted to settle a score.

The first set was a coin flip, with both players struggling to find their rhythm. At 2-1, Dart had three chances to break, only to let it slip. The next game, Boulter ruthlessly took advantage. That one break proved to be enough as the first set went her way in 47 minutes. But it was not pretty. Between them the pair had hit 40 errors.

Dart’s response? To reduce the mistakes and up her resolve. She broke early to lead 2-0, and again to move 4-0 up. And even though she then threw up a stinker of a service game – which included three double faults in a row – it did not ultimately matter.

It was now Boulter’s turn to fight back. But at 2-1 up in the final set she missed three break points – and looked to have paid the price when Dart broke her in the next game on the sixth attempt.

Boulter had never lost against a British opponent in a main tour match but that proud record was looking creaky at 2-4 and a break point down. But she survived and, at the third attempt, broke back to make it 4-4 in the final set.

Suddenly Dart started to wobble. One serve measured only 62mph and she was increasingly sending out distress signals. It seemed a matter of time before Boulter took advantage. But she was swimming in adrenaline – and paid the price.

“I’m an aggressive player,” she said. “I’m not going to sit back and just make the court. It’s not who I am and what I do. It’s tennis. You win some, you lose some. Today I lost. Made a lot of errors. But it is what it is.”

Earlier in the day there was disappointment for another Briton as Lily Miyazaki, lost 6-0, 6-0 to the 14th seed, Daria Kasatkina, in the second round.

Kasatkina was a 100-1 outsider for this tournament, but she knows her way around grass and could meet Raducanu later in the tournament. Her game was certainly too good for Miyazaki, who hit 31 unforced errors and seven winners.