Cameron Meyer and Callum Scotson fell just short of claiming gold in the men's Madison, going down by four points to French duo Benjamin Thomas and Morgan Kneisky as Belgium's Moreno De Pauw and Kenny De Ketele took bronze.
The UCI introduced a modified format for the Madison, with sprints after every ten laps of the 200-lap race instead of every 20.
“That ranks as one of the hardest I have done,” Meyer said. “We didn’t quite know how the new format would go at this level, sprinting every ten is one of the hardest things I have done.
“So I am so happy to stand on the podium, that is one of the hardest events, it is gruelling, it requires everything.
“We weren’t far off gold, to win a silver with Callum just caps off a great week.”
The medal elevated Meyer to fourth on the all-time list for most world championship crowns behind Koichi Nakano (10), Chris Hoy (11) and Arnaud Tournant (14).
A total of four world titles were awarded on the final day with France winning two, and Germany and Britain each claiming one.
Australia finished top of the medal table with three golds and 11 medals in total. France's final-day heroics saw them leapfrog Russia to finish second. France, who claimed five medals in total, and Russia both won three golds.
A late surge from Britain's Barker, a team pursuit Olympic champion, saw her snatch the points race title from United States' Sarah Hammer. Kirsten Wild of the Netherlands won the bronze medal, two laps in arrears.
Along with her points race victory, Barker also won scratch and Madison silver.
Germany's two-time Olympic champion Kristina Vogel did just about enough to retain her keirin title, and in the process win her ninth world title, finishing 0.061 seconds quicker than Colombia's Martha Bayona. Nicky Degrendele of Belgium won bronze.
In the men's 1km time trial, France's world record holder Francois Pervis won the event for the fourth time, finishing comfortably ahead of Czech Republic's Tomas Babek and Frenchman Quentin Lafargue, who tied for silver to the thousandth of a second.
This is only the second time the world championship has been held in Asia, with 11 countries winning world titles.