In Sunday's final, Kontaveit will bid to win a third title in as many months after beating Marketa Vondrousova 6-3, 6-4 in the other semifinal match.
Kremlin Cup 2021: Aryna Sabalenka knocked out by Ekaterina Alexandrova, Maria Sakkari beats Simona Halep
Sabalenka was playing in her first tournament since reaching the semi-finals of the US Open last month. She then missed the tournament in Indian Wells, California, after a positive test for the coronavirus.
The Scot, 34, won seven straight games en route to a 4-6, 6-3, 6-2 comeback victory in two hours and 24 minutes.
Shapovalov has now dropped three matches in a row, at Wimbledon and last month in the Swiss alpine village of Gstaad where he was top seed.
After knocking out World No 1 Novak Djokovic in the semi-final, Zverev, 24, beat Russia's Karen Khachanov in straight sets to win the men's Olympic gold medal in Tokyo earlier this month.
Top-seeded Russian Medvedev opened his week in the second round after a bye and staged a fightback to overhaul Kazakh Alexander Bublik 4-6, 6-3, 6-4.
Tokyo Olympics 2020: PV Sindhu's inspired performance earns bronze for India in badminton; men's hockey team enters semis
Check out photos from Day nine of Tokyo Olympics 2020
Tokyo Olympics 2020: Alexander Zverev eases past Karen Khachanov in straight sets to clinch men's singles gold
The fifth-ranked German overwhelmed Russian opponent Karen Khachanov 6-3, 6-1 at the Tokyo Games on Sunday for the biggest title of his career.
Tokyo Olympics 2020: 'Expect the unexpected', Twitter in awe of Alexander Zverev as he upsets Novak Djokovic
Here are a few reactions on Twitter after Zverev's shocking win over Djokovic
The World No 1 collapsed from a set and a break ahead as German fourth seed Zverev won 1-6, 6-3, 6-1 to set up a Sunday final against Russian Karen Khachanov.
Wimbledon 2021: Roger Federer, Novak Djokovic's regular appearances aside, record number of first-timers in QF at SW19
There will be a record 12 first-time Wimbledon quarter-finalists this year — two more than the previous best in 2014. Six appear on the men's side and six on the women's.
With an aggressive style that's built for grass courts, Korda got past Britain's Dan Evans 6-3, 3-6, 6-3, 6-4 to become the youngest US man to reach the round of 16 at the All England Club since Andy Roddick got to the semifinals in 2003.
French Open 2021: Kei Nishikori says he feels like he’s ‘played five matches already’ after winning back-to-back five-setters
Nishikori needed four hours to see off Russian 23rd seed Karen Khachanov 4-6, 6-2, 2-6, 6-4, 6-4 on Court Philippe Chatrier. In the first round, he also needed four hours to beat Italian qualifier Alessandro Giannessi.
Lyon Open: Cameron Norrie beats Karen Khachanov in straight sets to set up final against Stefanos Tsitsipas
In Sunday's final, the 22-year-old Greek will face Britain's Cameron Norrie who raced past Karen Khachanov 6-1, 6-1 in the other semi-final.
Greece's Tsitsipas eased past Japan's Yoshihito Nishioka 6-3, 6-4 in 66 minutes for a career best 31st win of the season.
Herbert, better known as a doubles specialist, swept past Australian Open semi-finalist Tsitsipas 6-7 (6/8), 6-4, 6-2.
Stefanos Tsitsipas will next play another Russian in fourth seed Andrey Rublev who battled past French qualifier Jeremy Chardy 7-6 (7/2), 6-7 (2/7), 6-4.
Stefanos Tsitsipas edges past Hubert Hurkacz to set up quarter-final clash against Karen Khachanov in Rotterdam
The Greek second seed dropped the second set but won in a tight decider on his third match point, securing a 6-4, 4-6, 7-5 victory.
Big-hitter Khachanov eased through the match without dropping a service game to eighth seed Wawrinka.
Paris Masters 2020: Karen Khachanov knocked out in first round as tournament begins despite France lockdown
Tournament organisers had expected to welcome 1,000 fans a day to the event, but instead had to refund the tickets when French President Emmanuel Macron announced France would re-enter lockdown last week.