Kuerten fought back, surviving two match points and seven deuces to hold serve and trail 5-4.
Ancic and Ljubicic finally converted the second of two match points at 5-4 up to clinch victory.
Serving at 4-5 and down two match points, the world No. 1 blistered three straight points to square it up.
"Anytime you can reach the quarter-finals it's great, " said Reeves, who survived two match points to force the second-set tiebreaker.
But Ricketts regained the initiative and, after two match balls, sealed the third to win 11-7 6-11 11-7 6-11 11-9.
Hingis endured a nervous second set, letting a 4-1 lead slip and wasting two match points on Safina's serve at 5-3.
Some bookmakers stopped taking bets on the League Two match on Friday after a high number of bets on Bury to win.
In Division Two, Doyle Motors Bruisers faced Kingspin in the first of a consecutive two match battle to take the runners up spot.
They will take charge on Wednesday, with caretaker boss Simon Clark staying in charge for Tuesday's League Two match at home to Notts County.
Coming off two match points, five-time Open champion Roger Federer lost to third-seeded Novak Djokovic in a riveting five-set semifinal match, 5-7, 6-1, 7-5, 6-2, 7-5.
The third set went the distance, with Czink fighting back from a break down before saving two match points at 4-5 and then forcing a tie-break.
Meanwhile work is under way to ensure that the two match venues in the city - Ellis Park and Soccer City - are ready on time.
French Open champion Kuznetsova visibly tired in the decider, as both players struggled to hold serve, but she saved two match-points before hitting a forehand wide.
The suspension rules Thomas out of the round two match against Munster at The Gnoll on 31 October, and Wales' international with South Africa on 6 November.
BBC: SPORT | Rugby Union | European Club | Lengthy bans for Heineken Cup duo
Federer held two match points in the second set tiebreak but they both went begging as Berdych won a thrilling match 3-6 7-6 6-4 against the five-time champion.
The 23-year-old then had two match points on Ilhan's serve, but the first was saved after the Briton's forehand was too long before the Turk saved the second with an ace.
Officers have said the outbursts may have been organised by fans claiming to support Cardiff, who won their opening division two match 1-0 against Wycombe at Ninian Park earlier on Saturday.
Seeded third in the absence of Novak Djokovic, Andy Murray and Juan Martin Del Potro, the world No. 6 saved two match-points as he clinched his 20th ATP Tour title in Doha.
"At 5-1, I went into the zone and I felt really strong and I just fought my heart out, " said Baltacha, who still had to save two match points in the breaker.
Lendl did not win another game as Chang closed out the match, but it was another unconventional tactic which sealed his victory as he forged two match points on his opponent's service.
Jankovic showed her class to move ahead with two aces in a row but Robson thrilled the home crowd by fending off two match points with a heavy serve and a big forehand.
The title had looked like it might slip away when Federer saved two match points in the fourth set, the second with a superb backhand, but Nadal said he had not been worried.
Officers said the outbursts on Saturday may have been organised by fans claiming to support Cardiff, who won their opening division two match 1-0 against Wycombe at Ninian Park earlier in the day.
Two-time Indian Wells champion Daniela Hantuchova saved two match points at 5-6 down in the third set of her second round meeting with Yanina Wickmayer before she edged through 5-7 6-3 7-6 (7-4).
Errani saved two match points in a game that the Italian produced a couple of the deftest drop shots you could wish for, but the Italian's resistance was finally ended when the Russian converted her third championship point.
Sharapova held serve and then denied Clijsters on two match points but there was no stopping the 27-year-old who, after two hours and 27 minutes, secured her 38th career singles title following victories this year in Brisbane and Miami.
BBC: Kim Clijsters beats Maria Sharapova in Cincinnati final
The third is Brian Lara, who holds records for the highest-ever score in first-class cricket (501 not out), and in Test matches (375), and who returned to his best form in the recent series against Australia with two match-winning innings.
His foul tackle on Liverpool midfielder Dietmar Hamann, during a Uefa Champions League match last December, landed him a two-match ban.
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