Romo threw for 506 yards and five touchdowns, the first 500-yard game in Dallas history, but was intercepted by Danny Trevathan at the Dallas 24 in the final 2 minutes to set up Prater's winning kick.
The Broncos (5-0) got all the way down to the Dallas 1, then drained the clock to make sure Prater's kick was the final play in a wild game.
The teams combined for 1,039 yards of total offense in the second-highest scoring game in regulation since the NFL-AFL merger in 1970, according to STATS.
Cincinnati and Cleveland combined for 106 points in the Browns' 58-48 win in 2004.
Manning, who threw for 414 yards, answered by leading a nine-play, 73-yard drive to Knowshon Moreno's tying 1-yard score with 2:44 remaining.
The Cowboys were on the verge of getting blown out early in the second half when they finally stopped Manning and forced a field goal. They later ended his streak of 227 passes without an interception when Morris Claiborne picked him off late in the third quarter.
Dallas converted the turnover into a 41-38 lead on Romo's 10-yard pass to Jason Witten, who had 121 yards receiving and a touchdown.
The Broncos answered with a drive to Prater's tying 50-yard field goal.
The biggest momentum swing came on Romo's 82-yard touchdown to rookie Terrance Williams that cut Denver's lead to 35-27 in the third quarter.
The Cowboys jumped ahead 14-0 in the first quarter.
But the Dallas defenders just couldn't stay with Denver's receivers, and then Manning fooled them and the 92,758 watching his first game at the $1.2 billion home of the Cowboys with a bootleg for an easy 1-yard score and a 28-17 lead.
Denver lined up for what looked like a run on third down from the 1.
But Manning had faked the handoff, and the roar from thousands of orange-clad Denver fans grew as they realized he was jogging toward the left corner of the end zone.
Romo got Dallas in position for a 48-yard field goal by Dan Bailey just before halftime with a 38-yard completion to Williams, who had 151 yards receiving.
Bryant had six catches for 141 yards and two touchdowns.
Julius Thomas led the Broncos with 122 yards and two scores, Moreno had 93 yards rushing.
Manning broke the record for TD passes through five games with his 19th on a 9-yard toss to Thomas in the second quarter. Daunte Culpepper of Minnesota held the previous mark with 18 in 2004.