Washington's offensive acquisitions paid quick dividends. Quarterback Smith completed 21 of 30 passes for two touchdowns without an interception, and Peterson carried 26 times and scored a touchdown. He caught two passes for 70 yards and lost a fumble.
The result was fifth-year head coach Jay Gruden's first opening week win.
Sam Bradford's Cardinal debut was less inspired. He finished 20 of 34 for 153 yards and one interception. Larry Fitzgerald had seven catches for 76 yards.
After Christian Kirk returned a punt to the Washington 26, the Cardinals had a chance to pull closer, but Ricky Seals-Jones couldn't hold Bradford's fourth-down pass in the end zone.
Washington, which ranked 31st in third-down conversions a year ago, succeed on 6 of 13 Sunday while the Cardinals were 1 for 8.
Smith capped an 11-play, 80-yard drive when he found Thompson for a 13-yard catch-and-run touchdown on the first play of the second quarter.
Peterson scored from 1 yard out to finish a 73-yard drive with 4:10 left in the first half, and Washington wasn't done.
After the Cardinals went three-and-out, the Redskins took over on their own 8-yard line, and Smith passed to Peterson for 18 yards to the Arizona 44 at the 2-minute warning. An unnecessary roughness penalty later gave Washington a first down on the 12, and three plays later, Smith hit tight end Jordan Reed for a 4-yard touchdown.
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