Stewart picked a good time to log his initial win of the season, jumping seven spots in the Sprint Cup rankings to second. He now trails Monday's second-place finisher Kevin Harvick by just seven points.
The two-time series champion conserved fuel down the stretch and held off Harvick to win by 0.9 seconds in a race rescheduled from Sunday due to persistent rain.
A poor second half of the season meant Stewart had to squeak into the 12-driver Chase. His last Sprint Cup win came last October in Fontana, Calif.
Dale Earnhardt Jr. staged a late charge through the field to grab third place in the initial Chase event.
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