Rodgers sent the Packers ahead with a 1-yard run early in the final quarter and threw a 2-yard scoring pass to Spencer Havner less than 3 minutes later.
Mason Crosby kicked a 48-yard field goal in the second quarter for Green Bay (5-4).
Rodgers completed 25-of-36 passes for 189 yards.
Green Bay's Charles Woodson turned in eight tackles and a sack, forced two fumbles and intercepted a pass.
Romo finished with 24 completions in 39 attempts for 105 yards.
Williams caught five passes for 105 yards.
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