Van Gisbergen's tally consisted of a try, four penalties and three conversions, as the champions stepped on the accelerator in the second half, having only boasted a slender lead at the interval.
Seond-half tries from scrum-half Rob Howley, Van Gisbergen and replacement scrum-half Peter Richards helped the hosts home, after their first-half scoring as restricted to three penalties.
Leeds scored the only try of the opening half when England 'A' fullback Dan Scarbrough went over on the half hour, Scotsman Duncan Hodge converting.
But they could not break down the resolute Wasps defence, and a penalty from Australian Tim Walsh was all they had to show for their efforts in the final half, as they made it two defeats from two for the season after losing to Bath on the opening day.
For London Wasps:Tries: Howley, Van Gisbergen, RichardsCons: Van Gisbergen 3Pens: Van Gisbergen 4
For Leeds Tykes:Try: ScarbroughCon: HodgePen: Walsh