Woods, who is expected to lead the British freestyle skiing team's charge at Sochi 2014 in February, produced a best score of 72.80 from the two runs in the final in Copper Mountain.
That comes after a second place at the season opener in New Zealand in August with Haatveit, who didn't compete in Cardrona, scoring 92.80 for his first win on just his second World Cup start.
Freestyle skiing slopestyle is a new addition to the Olympic programme for Sochi 2014 with athletes judged on the tricks they perform on a variety of obstacles on the slope including rails, quarter-pipes and jumps.
Given its new Olympic status it is hard to judge who will and won't be competitive in Russia with athletes picking and choosing when they compete but Woods is still on form.
An X Games bronze medallist and World Championships silver medallist last season, he is currently placed third in the overall World Cup standings with 104 points.
Nick Goepper, second behind Haatveit in Copper Mountain, leads the way with 180 while Russell Henshaw, third in Colorado, is second with 120 and then comes Woods.
In the women's slopestyle World Cup, Dara Howell leads the way having upgraded her second at the opener in New Zealand to first in Copper Mountain with Darian Stevens second and Grete Eliassen third.
Two more World Cups will be held before the start of the Olympics in Breckenridge and Gstaad with the season finale coming in Silvaplana towards the end of March.