Kiwis Karen Holliday (gold, 1990), Sarah Ulmer (bronze, 1999), Cath Cheatley (bronze, 2007) and Lauren Ellis (silver, 2010) have medalled in the women's event.
Scully and van Velthooven joined the gold won by team sprinters Ethan Mitchell, Sam Webster and Eddie Dawkins and bronzes awarded to the team pursuit and individual pursuiter Marc Ryan.
"In-house competitiveness creates the self-policing to fire us up," van Velthooven said.
"The London Olympics opened our eyes to the fact we can win world titles. Boys being boys, we try to beat each other at all times on the track. We draw blood and spew up in training so on race day we're ready because we've gone harder beforehand."
Van Velthooven took silver in the kilo last year and bronze in 2012.
The London Olympic keirin bronze medallist completed the non-Olympic 1000m event in 1m 00.518s, edging fourth place by 0.015s. He was 1.133 seconds behind French gold medallist Francois Pervis.
Van Velthooven was disqualified in the second round of the keirin on Friday for fractionally passing the back wheel of the derny bike which paces the riders.
"I was puzzled not to get a warning. I was disappointed but angry enough to get myself up to medal with a fresh mind in the kilo. By the third lap, I was humming, but the last lap was my strongest."
Scully, 24, has returned to the track after suffering a serious injury when he crashed into a lamp-post in a sprint finish during the 2010 Tour of Ireland.
After nearly a year out recovering, he moved to the road in Europe but returned to the track in November with strong performances at the Oceania Championships.
New Zealand head coach Dayle Cheatley said Scully enacted his plan perfectly by breaking the 40km non-Olympic race into segments.
"The first third was to get established, then he wanted to gain a lap - he got two - before hanging on at the end through the final 20 laps.
"It is a reflection of years trying to up our work ethic by pushing each other on a daily basis. We didn't come with a medal target, it was more an expectation of our athletes. Those have been met."
Aaron Gate remains in contention to defend his omnium title. At halfway, he sits fourth on 21 points with the individual pursuit, scratch race and kilo time trial to race today. French rider Thomas Boudat leads on 12 points.
New Zealand earned three medals at last year's world championship in Belarus - a gold to Gate in the omnium and silvers to van Velthooven in the kilo time trial and Mitchell, Webster and Dawkins in the team sprint.
