At the classic Old Course at St Andrews in Scotland, McIlroy and Hovland went straight to the fourth hole.
Then Hovland put in a bogey, which put McIlroy in the lead alone.
He was then able to extend that lead to two strokes already in the subsequent hole with a birdie.
Hovland continued to play doubles and could soon see himself passed by Australian Cameron Smith who had a super round on Sunday.
After 13 holes, he had hit six birdies and was here and there in a split lead with McIlroy.
Smith put home another birdie in the 14th hole, it was his fifth on as many holes, and then went up in the lead alone.
When Smith then put the eighth birdie of the day on the 18th hole, he went to 20 under par, two kinds of lead against McIlroy.
This meant that the Northern Irishman would need an eagle to force a special game for the title.
But McIlroy's rash put him in a position to chip for the eagle, a task that became too tough.
It secured the first major victory for Cameron Smith, who previously won five times on the PGA Tour and came second in a major tournament (2020 The Masters Tournament).
- Geez, what a week.
I know I will collapse here soon.
My team and I have put in so much hard work, but this one definitely makes it worth it, said a grateful Cameron Smith shortly after receiving the trophy.
Viktor Hovland finished in a shared fourth place in 14 under par, together with Tommy Fleetwood.
Rory McIlroy came in third, 18 under par, after American Cameron Young passed by an eagle on the 18th hole and finished at 19 under par.