Story (18-8) bested Nelson (13-1-1) over the course of five rounds at the Ericsson Globe Arena, handing his opponent the first pro loss of his career.
Story used constant pressure and a devastating left hand to press the pace from start to finish. Nelson stood firm in the pocket and returned fire, but he landed only single blows while Story was moving forward with combinations.
Nelson's blows did draw a small stream of blood over Story's right eye, but the cut never became an issue.
Nelson never got to use his vaunted submission skills as he simply couldn't get Story to the floor. In the end, Story outstruck Nelson 193-53, according to a FightMetric report.
"Normally when you hit an opponent, they show some emotion," Story joked after the fight. "He's got the toughest poker face in the sport."
In a surprising array of scores, two judges scored it 50-44, 49-46 for Story while the other had it 48-47 for Nelson.
In the co-main event, 20-year-old Hawaii bantamweight Max (Blessed) Holloway (11-3) ran his win streak to four, stopping New York-based Swede Akira Corassani (14-6-1) via TKO at 3:11 of the first round.
Corassani was the aggressor at the start, darting in and out of range with crisp strikes that frustrated his opponent. But Holloway kept busy on his feet by searching for opportunities and the work paid off with a straight right hand that sent Corassani toppling to the floor.
Holloway swarmed with additional punches, hunting for the finish. A gritty Corassani crawled back to his feet and tried to slow things down in the clinch, but Holloway broke away and continued his barrage of strikes for the victory.
"I'm feeling blessed right now," Holloway said after the win. "I just can't wait for the next one. The fight went faster than I thought it would, but I'm not going to complain."
Polish light-heavyweight Jan Blachowicz (18-3) made an immediate impact in his UFC debut, downing Ilir Latifi (10-4) in less than two minutes.
Blachowicz was measured in his attack, opening the fight by firing off kicks to the legs and body. As he gained confidence, the strikes gained steam and he connected with a crushing kick to the body that sent Latifi reeling.
Blachowicz followed with a grazing head kick that sent Latifi to the floor. As he covered on the canvas, Blachowicz unleashed a flurry of punches that forced referee Grant Waterman to call off the fight at 1:58 of the first round.
"I feel great," Blachowicz said after the win. "This is a dream come true.
"I want to show fans all over the world the legendary Polish power. I did it, and this is just the beginning."
In the opening fight on the main card, English featherweight Mike Wilkinson (9-1) scored a massive upset over highly touted Swedish prospect Nicklas Backstrom (8-1).
Backstrom looked the better fighter early, and he scored with a high kick and a pair of knees that seemed to wobble his opponent. But as he moved forward for the finish, Wilkinson drilled him with a right hand and Backstrom crashed to the floor.
Wilkinson jumped on top and continued to punch away until referee Bobby Rehman called a halt to the fight at 1:19 of the opening round.
"He said he was being matched up to win. He disrespected me," Wilkinson said after the fight. "There was no reason to disrespect me. There was no way I was stopping until I knew I had him and the ref stopped it."
The card was one of two UFC events on the day, coming before a televised event in Halifax. Welterweight Rory (Ares) MacDonald, a native of Kelowna, B.C., fighting out of Montreal, was scheduled to meet American-based Belgian Tarec (Sponge) Saffiedine in the main event.