TAMPA, Fla. (AP) — Joey Galloway slowed to a trot, holding the football in his hand like a loaf of bread.

Teammates screamed from the sideline, urging him to secure the ball, and Tampa Bay coach Jon Gruden cringed. It didn’t matter. The New Orleans Saints never seem to be able to catch up with Tampa Bay’s speedy receiver.

‘‘I know that bothers guys, but it works for me,’’ Galloway said after tormenting the suddenly defenseless Saints with four catches for 135 yards and two touchdowns in a 31-14 Buccaneers victory Sunday.

Galloway practically walked into the end zone to finish a 69-yard scoring play in the second quarter, then added his 10th TD in six meetings between the NFC South rivals on a 24-yard catch that made 21-0 just before the half.

The Saints (0-2) were embarrassed for the second consecutive week and have been outscored 72-24 after having one of the NFL’s most explosive offenses and reaching the NFC championship game last season.

Before Mike Karney scored New Orleans’ first offensive touchdown of the season on a 1-yard run late in the third quarter, the Saints had surrendered 62 unanswered points to the Bucs and Super Bowl champion Indianapolis, which beat them 41-10 last week.

‘‘I’m very surprised. We really need to take a deep look at ourselves, identify the problems and figure out how to fix it,’’ New Orleans quarterback Drew Brees said.

‘‘I think we have the ability to be a very good offense. One of the best, if not the best, in the league. Unfortunately we’re not playing like it right now.’’

Jeff Garcia completed 10 of 16 passes for 243 yards and no interceptions for the Bucs (1-1) after not getting his team into the end zone during a season-opening loss to Seattle. He was not sacked, and Tampa Bay had no turnovers.

Galloway has had some of his best games as a Buccaneer against New Orleans with 23 receptions for 473 yards and nine TDs in six meetings. He also returned a punt for a touchdown against the Saints in 2004.

‘‘I don’t think anyone really gave us a chance to win this game except ourselves. … We have to build on that,’’ Galloway said. ‘‘We didn’t play our best game, but we played a good one.’’

Brees finished 26-of-44 for 260 yards with one touchdown. He was intercepted once and sacked twice.

The Pro Bowl quarterback set up Karney’s TD with a 58-yard completion to David Patten and threw a 4-yard scoring pass to Marques Colston late in the fourth quarter. However, Brees never got into a rhythm against the Tampa Bay defense.

The Bucs forced two turnovers, converting Deuce McAllister’s first-quarter fumble and Cato June’s third-quarter interception into touchdowns.

Neither team scored an offensive TD in its season opener, the Bucs limited to a pair of field goals in a 20-6 loss to Seattle and the Saints only getting into the end zone on Jason David’s fumble return during New Orleans’ loss to the Colts.

The Bucs signed Garcia in March, finally giving Gruden a quarterback who fits the Bucs’ version of the West Coast offense. The three-time Pro Bowl selection’s ability to make plays on the run was especially attractive to Gruden, who has started eight different QBs since arriving in Tampa Bay in 2002.

Garcia extended Tampa Bay’s first touchdown drive, scrambling for 7 yards on third-and-6 to the New Orleans 1. Williams, limited in practice all week because of bruised ribs, scored two plays later.

‘‘No disrespect to the previous quarterbacks we’ve had here, but the biggest play of the football game was Garcia scrambling on third down,’’ Gruden said. ‘‘He went in head first, trying to get the first down. … It sends a message. … I think it’s a healthy, exciting change.’’

Galloway picked up a key block from receiver Michael Clayton on his long catch-and-run TD, sprinting into the clear as he crossed midfield. On his second touchdown, he cut in front of stumbling safety Josh Bullocks and was wide open in the middle of the end zone.

The Saints had some success moving the ball on the ground early, but eventually had to abandon the running game. McAllister had nine carries for 47 yards at the half, but only carried once for 2 yards the rest of the way.

Meanwhile, Tampa Bay also did a good job of containing Reggie Bush, limiting the Saints’ multi-purpose threat to 27 yards on 10 rushes and 43 yards on six receptions.

‘‘I’m disappointed. I’m not surprised,’’ Saints coach Sean Payton said.

‘‘We didn’t play well enough. It’s going to be hard to win in any game if you’re putting it on the ground, giving up big plays behind you. … We’ll get it corrected, I’m confident.’’