World number three Medvedev was the top seed for this week's tournament following his run to the Australian Open final but was dumped out 7-6 (7/4), 6-4 in just over 90 minutes by Serbian Lajovic, currently ranked 27th.
German Zverev was seeded third in the tournament but was surprised by 43rd-ranked Bublik in just one hour, 19 minutes.
Popyrin started off badly, losing the first set 4-6 but charged back and snatched the second 6-0.
Singapore Open: Australia's Alexei Popyrin ousts third seed Marin Cilic to enter maiden ATP Tour final
Popyrin let out a huge roar after sealing his victory in front of 250 fans, who were allowed to attend the tournament after passing COVID-19 tests.
Third seed Cilic, who received a bye in the first round, ended a four-match losing streak since November to remain on course for his 19th ATP singles title.
Antalya Open: Australian Alex de Minaur claims fourth career title after Alexander Bublik retires with ankle injury
The fourth-seeded De Minaur led the eighth seed 2-0 in the first set when his Kazakh opponent retired due to a right ankle injury he suffered in his semi-final.
Open 13 Provence 2020: Stefanos Tsitsipas sets up final against Felix Auger-Aliassime after 7-5, 6-3 win against Alexander Bublik
Defending champion Stefanos Tsitsipas reached the Open 13 final with a 7-5, 6-3 win against Alexander Bublik.
Open 13 Provence 2020: Daniil Medvedev bows out in quarter-finals after third straight loss to Gilles Simon; Stefanos Tsitsipas advances to semi-finals
Medvedev, the US Open runner-up and the top seed in Marseille, dropped his serve five times against the 35-year-old Simon, after breaking him in the first game
Rotterdam Open 2020: Unseeded Slovenian Aljaz Bedene upsets World No 6 Stefanos Tsitsipas in straight sets to book quarter-final spot
Russian Andrey Rublev continued his impressive form with a 7-5, 6-3 victory over Alexander Bublik to extend his win record in 2020 to 13-1
Newport Open: John Isner beats first-time finalist Alexander Bublik in straight games to win fourth title
Isner converted all three of his break points in the game, including on match point when the Kazakh failed in his bid to catch the American with an underarm serve on the final point.
Newport Open: Three-time champion John Isner reaches final after hard-fought win over France's Ugo Humbert
Three-time champion John Isner fended off fourth-seeded Frenchman Ugo Humbert 6-7 (4/7), 7-6 (7/5), 6-3 Saturday to reach the final of the ATP grass court tournament
French Open 2019, men's singles roundup: Novak Djokovic cruises into third round; Dominic Thiem weathers tough spell to proceed
Fourth seed Dominic Thiem, who reached the final at Roland Garros last year, had to use his full range of shots to overcome 91st ranked Bublik, who put up a fight against the prince of clay.
Murray has been nursing a sore hip he sustained during his French Open semi-final loss to Stan Wawrinka in June.
Top seed Andy Murray downed Alexander Bublik 6-1, 6-4, 6-2, shrugging off two brief rain delays and showing little sign of the hip problem which had plagued him in the build-up.
Murray, a two-time Wimbledon champion, will play the first match on Centre Court on Monday against Kazakhstan's Alexander Bublik.