“If it wasn't for the crowd, I don't think I would have won today”
Germany's Kristina Vogel won her third title of the weekend, beating world champion Becky James in the keirin.
Olympic champion Jason Kenny, who finished fourth in Saturday's men's keirin, was eliminated in men's sprint qualifying - normally considered a formality for top British riders.
GB team-mate Matt Crampton came through qualifying but was defeated in the semi-finals by two impressive rides from Trinidadian 22-year-old Njisane Phillip.
Crampton, 27, lost out to Australia's Shane Perkins in the bronze ride-off while Germany's Robert Foerstemann beat Phillip to gold.
Jon Mould, riding for Welsh trade team USN, took bronze in the non-Olympic men's scratch race.
Trott, the reigning Olympic and European champion in the omnium as well as the world silver medallist, once again thrilled her home crowd as she dominated Sunday's events.
The Hertfordshire rider was sixth overnight but finished second in the individual pursuit before coming first in the scratch race, lapping the group, and winning the time trial finale.
Omnium results are calculated by adding up each rider's positions across the six events - Trott's tally of 19 points left her four points clear of Canada's Gillian Carleton in second.
"If it wasn't for the crowd, I don't think I would have won today," Trott told BBC Sport.
"Taking a lap [in the scratch race] is so hard but I was so far behind. It was a risk I had to take.
"Going into the race I was six points behind Gillian. I didn't really have a choice. I just thought, if I didn't make it, at least I tried."
Simon BrothertonBBC Sport cycling commentator
"This is a healthy position for Great Britain to be in. Jason Kenny wasn't on top form, but he performed to the level he'd been doing in training. He is where he is, he wasn't under-par from their point of view.
"There's a lot of encouragement, too. I'd like to pick out Katie Archibald from Scotland. She got a silver medal in the scratch race and a bronze in the individual pursuit.
"She won the European title with the pursuit team a couple of weeks ago - she's had a taste of being in that senior team and I think she's a really exciting young talent."
In the women's keirin, James proved helpless to stop Vogel, already the World Cup champion in the individual and team sprints, as the in-form German rolled around the outside to take victory.
"I knew I wouldn't be able to beat Vogel today," said Welsh rider James, 21.
"To get two wins in the first two rounds, and ride so well - I've made mistakes in the last two weeks of racing and I've corrected that. I've made massive improvements since [last month's] Europeans, hopefully I'll keep going that way."
Elsewhere on Sunday, Canadian Laura Brown won the women's points race with British duo Elinor Barker and Katie Archibald 11th and 15th respectively. Wales' Hayley Jones came 19th in Team USN colours.
Austria's world silver medallist Andreas Mueller hung on to beat Italy's Elia Viviani in the men's scratch race, providing a scintillating finale to the World Cup. Mould, 22, came third with fellow Briton Owain Doull 11th.
"Mueller really was strong. We were chasing and chasing, we couldn't reel him back," said Mould. "Another 10m, maybe."
Earlier, 16 of the 41-rider field had advanced to the first round of the men's sprint, but Bolton-born Kenny was not one of them after finishing in 10.154 seconds.
I am a bogeyman - Jason Kenny
The 25-year-old ended qualifying in 24th place as world record-holder Kevin Sireau also struggled, finishing last in 10.573.
"Having been up at the crack of dawn, having just done team sprint and keirin already at the weekend, you're clearly not going to be at your freshest," said British sprint coach Iain Dyer.
"We weren't really expecting Jason, who has been doing 10.1 (seconds) for the last month, to suddenly come in and do a 9.8."
Kenny must finish in the top 30 of the World Cup rankings, after this season's three stages, to ride in the event at February's World Championships in Cali, Colombia.
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