Defending champion Hellen Obiri, from Kenya, took the women's title in the 10k while Italy's Eyob Faniel triumphed in the men's event.
British Olympian Sir Mo Farah finished eighth in the penultimate race of his remarkable career.
Greater Manchester mayor Andy Burnham and Coronation Street stars also took part in the annual spectacle on a sunny day in the city.
Chosen as one of the event's official starters, Jess Dyer, who was diagnosed with clinical depression at the age of 13, described it as "emotional, overwhelming and incredible".
The race started as a legacy event from the 2002 Commonwealth Games
Other starters included Pete Wallroth, founder of the charity Mummy's Star, and Elaine Wilkinson, who has completed every event since its start in 2003, following the city's Commonwealth Games.
Paul Foster, chief executive of The Great Run Company, described the race as "humbling".
He said it was "an event that has always been an embodiment of everything that's great about Manchester. Grit, determination, diversity, pride and humour.
"We can't wait to see what the next 20 years will bring."
Sir Mo Farah and Hellen Obiri with the Campbell family who ran for a local hospital treating Hugo, aged two
John Hacking, executive member for leisure at Manchester City Council, said it was "brilliant to welcome runners, their families and their friends into the city centre".
He added: "Whether people are running for charity or in memory of loved ones, or to overcome individual challenges, every runner personifies the Manchester spirit."