The Olympic team pursuit champion added the points title to previous victories in scratch and individual pursuit, as well as her silver in the keirin.
Daniel Bigham also completed a hat-trick with gold in the team pursuit.
"I couldn't ask for more. I could only hold out for the three days; tomorrow I'll be in bed all day," Scotland's Archibald, 22, told BBC Sport.
Archibald fractured her wrist in November at the Glasgow World Cup and returned to competition only recently.
"I don't think the wrist injury has set me back too much, so I'm back on track now," she said.
Despite her progress, she said she would not travel to Los Angeles for the forthcoming UCI World Cup.
She added: "I don't think I'm going out [to LA]. I want to get back in the gym and recuperate the training block that I've missed without too much travelling and hopefully on to the World Championships in April."
Bigham, 25, who earlier in the meet won the individual pursuit and kilometre time trial, took the team pursuit title with Jacob Tipper, Charlie Tanfield and Jonathan Wale.
Other final-day winners at the National Cycling Centre included Dani Khan in the women's 500m time trial and Jack Carlin, Ryan Owens and Jack Truman in the men's team sprint.
Sophie Capewell and Lauren Bate-Lowe took gold in the women's team sprint and Ethan Hayter won the men's scratch race.
Katie Archibald won her third gold medal on the final day of the National Track Championships in Manchester.