Bevin beat state Rep. Robert Goforth, William Woods and Ike Lawrence.
Meantime, Democrat Andy Beshear, the state's attorney general, defeated two prominent rivals -- Rocky Adkins and Adam Edelen -- in the party's four-candidate primary.
The governor's strong showing on Tuesday gives him a boost heading into the fall campaign, in a state that has trended overwhelmingly toward the GOP.
Bevin tried to frame the November matchup Tuesday night, saying: "It's going to be a remarkably stark contrast between the two tickets -- conservative vs. liberal, black and white, night and day."
Beshear ripped into Bevin's policies on health care, pensions and education in his own preview of the fall campaign. "It is not about what's going on in Washington, D.C.," Beshear said in declaring victory. "And it's not about right vs. left. Folks, it's about right vs. wrong."
At least among Republican voters, Bevin overcame a series of self-inflicted political wounds from his feud with groups representing public school teachers. Bevin's approval ratings slumped after his failed attempt to change the state's struggling public pension systems.
Trump, in a tweet earlier Tuesday, encouraged Kentuckians to vote for Bevin on Tuesday, saying he "has done a fantastic job for you and America!"
After the race was called for Bevin, the president tweeted, "Matt, you are doing a fantastic job!"
The Associated Press contributed to this report.