Power held off Dixon in the closing laps of Sunday's event after Dixon had won Saturday's first race at Houston's Reliant Park.
The two weekend results enabled the two-time IndyCar champion to bypass Helio Castroneves by 25 points heading into the season-ending Oct. 19 race at Auto Club Speedway in Fontana, Calif.
As he did Saturday, pole-sitter Castroneves contended with gearbox problems and ended up finishing 23rd. He came into the weekend with an eight-point lead over Dixon.
The race was marked by a spectacular crash on the final lap when three-time IndyCar Series champion Dario Franchitti was involved in a wreck with drivers E.J. Viso and Takuma Sato that also injured 13 fans.
Franchitti was pulled from the car and hospitalized.
Team owner Chip Ganassi said the Scotsman was awake and alert but had sustained some injuries.
Two of the 13 fans also required hospitalization, fire officials said.