Hudson-Smith, who set a European record of 44.26 in winning his heat this week, went out hard and was well clear coming off the final bend but that effort took its toll as he began to tie up, allowing Watson to win in 44.22 seconds.
Hudson-Smith, the bronze medallist last year, took silver in 44.31, with American Quincy Hall also finishing strongly for bronze in a personal best 44.37.
Jamaica’s first gold in the event since Bert Cameron won at the inaugural World Championships 40 years ago came minutes after Danielle Williams (30) had taken the country’s first gold in Budapest in the women’s 100m hurdles.
Olympic champion and world leader Steven Gardiner of the Bahamas was not involved in the final having pulled up with a hamstring injury in the semis.
"I was a good race although I did not execute it as coach (Glen) Mills planned," said Watson. "In the last 50 I didn't look at other athletes, I was focusing on myself only.
"This is an amazing season for me. After winning the world youth title in 2017 it is amazing to win the gold medal at my first senior Worlds."
After coming so close to Britain's first gold in the event, Hudson-Smith revealed he had been struggling with injury for much of the season.
"Under the circumstances, I wasn’t even supposed to be here. I’ve had really bad Achilles tendonitis," he said.
"Sometimes I can’t walk, sometimes I can. I’ve been saying all year I just have to be perfect for three days.
"I got a bronze last year, I got a silver this year so next time gold."
Williams captures second hurdles title
Earlier, Jamaica's Williams (30) raced to her second world title in the women's 100-metre hurdles.
Williams, who won world gold in 2015 and bronze in 2019, edged Olympic champion Jasmine Camacho-Quinn of Puerto Rico, to win in 12.43 seconds.
Camacho-Quinn had to settle for silver in 12.44.
Less than a tenth of a second separated the top four hurdlers with American Kendra Harrison taking bronze in 12.46, keeping Devynne Charlton of the Bahamas (12.52) off the podium.
Rogers secures double hammer gold for Canada
Camryn Rogers (24) won the women's hammer throw on Thursday to secure a shock double gold for Canada after Ethan Katzberg (21) had claimed a surprise title in the men's event.
Rogers, silver medallist last year in Eugene, went one better in Budapest, winning with a throw of 77.22 metres.
Americans won silver and bronze with Janee Kassanavoid throwing 76.36 for second and teammate DeAnna Price taking third with 75.41.
Rogers, who won the Commonwealth Games title last year for her first major international win, claimed victory with her opening throw.
