Sinner and Ruud crash out in Cincinnati as Medvedev advances
On his 22nd birthday, he Italian, who triumphed in Toronto on Sunday, lost for the first time this season in an opening round after 13 winning starts.
The 33-year-old Lajovic, ranked 66th in the world was outstanding as he took full advantage of Sinner's fatigue after his efforts in Canada, winning all his 16 points at the net and all five break points he faced.
Lajovic, who beat compatriot Novak Djokovic in Banja Luka in April and has now had four straight wins against top ten opponents, said he was enjoying the benefits of a new approach.
"I’ve started changing a lot of things about me," he said.
"This year I started doing a lot of mental health training, with a therapist and everything, and I started to change some things about myself, which is always hard and especially when you are over 30.
"I was happy to finish in two sets because I know that going three sets against these kinds of players, it’s always going to be much tougher," he added.
It was also a disappointing day for fifth seed Casper Ruud, with the Norwegian going down 6-4, 3-6, 6-4 to Australian qualifier Max Purcell, ranked 70th in the world.
Daniil Medvedev started his Cincinnati campaign with a comprehensive win.
The number three backed up last week's victory over Lorenzo Musetti with a repeat performance, dispatching the Italian 6-3, 6-2 after also having beaten him six days ago in Toronto.
Medvedev turned in an efficient victory over Musetti as he lined up match point with an overhead smash and finished off with a service winner.
He advanced to the third round with 19 winners and 21 unforced errors while his opponent could manage just seven winners.
Medvedev has been the model of consistency, earning a tour-leading 23 match wins this season in Masters events, triumphs which have yielded Masters titles in Miami and Rome.
Last year's runner-up Stefanos Tsitsipas tamed the upset hopes of American Ben Shelton, defeating the 20-year-old 7-6 (7/3), 7-6 (7/2).
Elsewhere, Gael Monfils continued his run of comeback form, defeating Australian Alex de Minaur 7-5, 6-4 to reach a third round for the second consecutive week.
The 36-year-old Frenchman excelled as he beat the weekend finalist in Toronto in two hours with 29 winners to 14 for de Minaur.
Alexander Zverev, the 2021 champion, moved into a third-round showdown with Medvedev, putting out Japan's Yoshihito Nishioka 7-5, 6-4.
Toronto semi-finalist Tommy Paul was slotted in as the next opponent for top seed Carlos Alcaraz with a 6-1, 7-6 (7/4) defeat of Frenchman Ugo Humbert.
In the WTA draw, world number one Iga Swiatek raced to a 6-1, 6-0 sweep of American Danielle Collins to reach the third round on the first dry day of the week.
The Pole, who lost a Montreal semi-final to Jessica Pegula, defeated Collins last week and took just 61 minutes to do it again.
Top American Pegula relied on an angry racquet smash to reset her game after losing the opening set to Martina Trevisan of Italy.
The third seed, who won the Montreal title at the weekend, reversed her fortunes for a 6-7 (2/7), 6-2, 6-3 win to reach the third round.
"Sorry to my racquet," she said. "I was not so positive today, but the crowd really helped me out.
"It was a super-quick turnaround for me from Canada. Conditions here are very different and that's always going to be trouble. The ball really flies."
Tenth-seeded Wimbledon champion Marketa Vondrousova advanced past Anastasia Potapova 6-4, 6-2. She will next play American Sloane Stephens.
Venus Williams lost to China's Zheng Qinwin 1-6, 6-2, 6-1.