The 24-year-old clocked a person best 6.49seconds to hold off Nesta Carter and Marvin Bracy, with GB team-mate Dwain Chambers clocking 6.53 to finish sixth.
Earlier in the day Tiffany Porter won Great Britain's first medal of the competition with a bronze in the 60m hurdles.
Porter recorded a season's best 7.86 with Nia Ali taking gold ahead of defending champion Sally Pearson.
"I'm so honoured to bring a medal home for Team GB. I never take that for granted, anything can happen in these races," Porter said.
"It wasn't my best performance. My start was awful, that was frustrating because that's one of the better parts of my race. All of us know you never go out there thinking who ran what earlier. It's all about delivering on the day, Nia showed that."
Elsewhere in the afternoon session Luke Cutts finished eighth in the pole vault final with a best clearance of 5.65m.
Results from the World Indoor Men's 60m Final on Saturday
1. Richard Kilty (Britain) 6.49
2. Marvin Bracy (U.S.) 6.51
3. Femi Ogunode (Qatar) 6.52
4. Su Bingtian (China) 6.52
5. Gerald Phiri (Zambia) 6.52
6. Dwain Chambers (Britain) 6.53
7. Nesta Carter (Jamaica) 6.57
8. Kimmari Roach (Jamaica) 6.58
- Sports & Recreation
- Dwain Chambers
- Marvin Bracy
- Nesta Carter
- Tiffany Porter
- Great Britain