Kurt Warner threw for 338 yards and four touchdowns for the Rams (11-2), who remained a game ahead of NFC West rival San Francisco for the best mark in the conference.
With St. Louis' win -- its seventh in as many road games this season -- the 49ers also clinched a postseason berth. The Saints (7-6) had a pair of trick plays go awry and made their road that much tougher.
Bruce set a franchise record with his 54th touchdown reception, breaking the mark held by Hall of Famer Elroy "Crazy Legs" Hirsch, and added two more before being hobbled by a bad foot.
The Rams' air attack also forced a pass interference call deep in New Orleans' territory in the fourth quarter. The play followed a 15-yard roughing-the-passer call and sparked an ugly incident at the Superdome.
With St. Louis at the Saints 1-yard line, leading 31-21, fans began throwing bottles in the end zone, forcing players and officials to scatter. The incident led to 13 arrests and 15 ejections.
"I know these fans love their team, but there's a line that needs to be drawn," Warner said. "And I hate to see people go across it."
Sunday in Cleveland, a game between the Browns and Jacksonville Jaguars was delayed more than 40 minutes when fans littered the field with bottles after a call went against their team.
"I think the owners in Cleveland kind of condoned that type of behavior," Rams linebacker Mark Fields added. "So I think that it will carry over throughout the NFL."
Favorites to represent the NFC in the Super Bowl, the Rams are hoping their performance carries over the rest of the year. They finish the regular season with winnable games against Carolina, Indianapolis and Atlanta.
"We are not content right now," Fields said. "We know we want to have home-field advantage and get ready to play those playoff games."
Bruce got them that much closer to home-field advantage with TD catches of six, 11 and 40 yards. He had just three touchdown receptions all season before scoring for the first time since November 11.
"That's his game -- to get the ball and make huge plays at huge times," Warner said of Bruce, who finished with five catches for 83 yards before injuring his foot on his final TD grab.
While Bruce set a franchise mark, Warner approached an NFL record, recording his eighth 300-yard passing game of the year -- one off the league mark he matched in 1999.
Warner completed 23-of-32 passes without an interception.
"With all of the weapons that they have on offense, if you don't bring your 'A' game against a team like that, you can see the results," New Orleans defensive tackle La'Roi Glover said.
The Saints were whistled for 16 penalties, matching a franchise record for a home game, totaling 132 yards.
"It is hard to get something going when you have 16 penalties," Coach Jim Haslet said.
"That is not typical of us," added quarterback Aaron Brooks, who went 23-of-40 for 269 yards with three TDS and a pair of interceptions. "It is part of the game and it is something that we have to deal with."
The Rams were called for 11 penalties themselves, but they forced two key interceptions to offset their two fumbles.
New Orleans also had a pair of mental miscues on special teams.
After opening the scoring on Brooks' four-yard pass to Terrelle Smith, the Saints went for a surprise on-side kick, but touched the ball before it went 10 yards.
They also faked a field goal in the second quarter but missed a blocking assignment as kicker John Carney sprinted toward a first down.
"We were trying to do everything we could to win the game," Haslett said. "When you play a team like that, you try to do anything."
After consecutive TD catches by Bruce, New Orleans tied it at 14-14 on a six-yard pass from Brooks to Joe Horn late in the first half. But the Rams went 79 yards in 88 seconds and took the lead on Faulk's four-yard TD grab.
Bruce made it 28-21 with a 40-yard touchdown catch before Willie Jackson got New Orleans within 28-21 with a 28-yard TD grab. Jackson finished with eight catches for 156 yards.
Wilkins kicked a pair of fourth-quarter field goals to cap the scoring.