Jones finished with 30 completions in 51 pass attempts for 416 yards with one interception.
Broyles, by far his favorite receiver, made a school bowl-record 13 catches for 156 yards.
DeMarco Murray scored the game-winning touchdown on a 1-yard, third-quarter run.
Patrick O'Hara caught a touchdown pass, while both Travis Lewis and Quinton Carter had pass interceptions for the Sooners (8-5), who failed to score in the fourth period, but won three of their final four games.
Heisman Trophy candidate Toby Gerhart led Stanford with two touchdowns on 32 carries for 133 yards.
Owen Marecic ran for a touchdown, Nate Whitaker kicked two field goals, but Tavita Pritchard passed for just 118 yards with two interceptions for the Cardinal (8-5), who were making their first bowl appearance since 2001.
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