Jannik Sinner had to dig deep to get the better of Auger-Aliassime in the second semi-final.
Canada booked a showdown with Australia in the Davis Cup final after Felix Auger-Aliassime and Vasek Pospisil edged out Italians Matteo Berrettini and Fabio Fognini 7-6(2), 7-5 in a tightly fought decisive doubles affair on Saturday.
Shelton was broken in the opening and closing games of the first set, unable to take advantage of a break point at 2-1 down while Sinner was always capable of pulling out an ace at the crucial time, hitting two in that fourth game to hold serve.
World number two Jannik Sinner survived a stern test from Joao Fonseca on Tuesday to reach the Indian Wells quarter-finals.
Images from the US Open matches played at Flushing Meadows on Saturday
Lehecka struck eight aces and converted four of eight break chances to secure the first Top 3 win of his career.
Tallon Griekspoor staged a grand recovery, saving four match-points, before stunning top seed Daniil Medvedev 2-6, 7-6(7), 7-5 to reach the semi-finals of the Dubai Championships on Thursday.
With world number four Ruud already assured of a semi-final berth the match was in reality a dead rubber.
Canada began their Davis Cup Finals campaign in confident fashion as wins for Denis Shapovalov and Felix Auger-Aliassime assured them of victory
Medvedev in Shanghai semis as Rinderknech joins cousin Vacherot in last four
Jannik Sinner and Carlos Alcaraz are among the world's top players calling for the Davis Cup to return to its traditional home-and-away format and be staged over two years, a proposal backed by ATP chairman Andrea Gaudenzi.
The 38-year-old said he had been dealing with the injury throughout the tournament in Athens.
Canada powered into the quarter-finals of the Davis Cup for the third straight year with a victory over Britain on Sunday.
Ninth seed Auger-Aliassime, 21, was the dominant player in the first set and despite a wobble when serving at 6-5 he won a tiebreak courtesy of some Medvedev double-faults the Russian later blamed on the sweaty conditions.
Reigning Paris Masters champion Novak Djokovic beat Stefanos Tsitsipas in a three-set epic on Saturday to set up a title clash with Holger Rune, who reached his first ATP Masters 1000 final after a comfortable win over Felix Auger-Aliassime.
Alexander Zverev's Grand Slam experience proved decisive as the German third seed defeated Briton Jacob Fearnley 6-4 6-4 6-4 in the U.S. Open second round on Thursday
Coco Gauff started her quest for a maiden Australian Open title with a straight games win over Kamilla Rakhimova to reach the second round.
Zverev and Shelton tested each other in a high-quality encounter before the world number three played a near flawless tiebreak to clinch the match in little over two hours and stretch his career win-loss record over the American to 3-0.
Djokovic to face World number 204 Valentin Vacherot next.
Daniil Medvedev dominated Canada's Felix Auger-Aliassime 6-4, 7-5, 6-2 on Friday to reach the US Open final courtesy of a dozen aces in just a little over two hours.
Medvedev battles back to beat Ruusuvuori
Top seed Carlos Alcaraz withstood a charge from qualifier Luca Nardi for a 6-1, 4-6, 6-3 victory in the second round of the Qatar ExxonMobil Open in Doha on Wednesday.
Jannik Sinner's bid to win back-to-back Halle Open titles was ended on Thursday
Canada defeated Australia 2-0 to win its first Davis Cup title on Sunday
Carlos Alcaraz defeated Tallon Griekspoor of the Netherlands 6-1, 6-2 at the China Open on Sunday to capture his 200th career tour victory.
Images from Day 10 of the 2022 Australian Open in Melbourne on Wednesday.
Although hampered by a chronic foot injury that saw him out in the last 16 of the Italian Open, an event that precedes the French Open, the 21-time Grand Slam champion has looked pain-free in his bid for a 14th French Open crown.
Carlos Alcaraz, who advanced to the last eight in Cincinnati for the third time, has now won 36 of his last 38 matches.
Andy Murray started working with former coach Daniel Vallverdu this month on a short-term basis as the multiple Grand Slam winner works towards rediscovering the form that took him to the top of the world rankings.
Rafael Nadal trailed in the second set before overcoming No. 5 seed Cameron Norrie of Great Britain.
Italy's Sara Errani and Jasmine Paolini beat Mirra Andreeva and Diana Shnaider 2-6, 6-1, (10-7) to win Olympic gold in the women's doubles tennis on Sunday.
Zverev cruised past home favorite Roberto Bautista Agut 6-2, 6-2, while Sabalenka triumphed over qualifier Anna Blinkova 6-3, 6-4.
Holger Rune crashed out to Yoshihito Nishioka in the ATP 250 Adelaide International 1 first round.
Djokovic withdraws from Western & Southern Open, to 'turn focus on US Open.'
Building the stamina to consistently survive the rigours of playing five-set matches will top Andy Murray's agenda as the former US Open champion, who has undergone two hip surgeries, plots the revival of his career.
Factbox on Carlos Alcaraz, who beat Alexander Zverev
Auger-Aliassime, now coached by Nadal's uncle and long-time mentor Toni who sat in his box, will face Fritz in his final group match with a chance of making the last four.
Fonseca cruised through the first set before Fearnley found his groove in the second to level the match on a windy day in the California desert.
Novak Djokovic was stunned 7-6(4), 6-2 by Matteo Berrettini in the Qatar Open first round on Tuesday as the Italian enjoyed his first win over the former world number one.
Carlos Alcaraz got his grasscourt campaign up and running with a 6-4, 7-6(4) victory over Australian Adam Walton