Wigginton drove his 21st homer of the season just inside the right field foul pole off Scott Atchison, who came in after Clay Buchholz allowed one unearned run and four hits in six innings.
Bergesen (8-10) gave up one run and five hits as he allowed three runs or fewer for the ninth time in his last 10 starts.
Buchholz lowered his ERA from 2.48 to 2.39, second in the AL to Seattle's Felix Hernandez at 2.35. Atchison (2-3) allowed three hits and retired just one batter.
Wigginton's homer made it 4-1, and the Orioles added a run in the eighth on Robert Andino's sacrifice fly and four in the ninth off Jonathan Papelbon.
Boston took a 1-0 lead in the second on Daniel Nava's RBI single. Baltimore tied it in the sixth when Adam Jones, who had singled, scored from first with two outs on an error by second baseman Marco Scutaro when a very high popup by Felix Pie ticked off his glove and fell behind him.
The Red Sox had a chance to go ahead in the bottom of the sixth when Jed Lowrie walked with two outs and Ryan Kalish hit a drive to deep right-center. But the ball bounced into the stands for a ground-rule double, forcing Lowrie to stop at third. Nava then took a called third strike.
Cesar Izturis led off the top of the seventh with a single and was forced at second on a grounder by Brian Roberts. Nick Markakis singled and Wigginton hit Atchison's first pitch to him for a homer.
The Red Sox threatened in the seventh with two outs and runners at first and third, but David Ortiz struck out for the 54th time in 170 at-bats against lefties when he looked at a third strike from Michael Gonzalez.
Bergesen allowed one hit in his last three innings — Kalish's double in the sixth. In his last start on Sept. 15, a 3-1 win over Toronto, he pitched his third career complete game. His ERA over his last 10 starts is 2.31.
Buchholz struck out five and gave up four hits and three walks but allowed runners in each of his innings. In three of them, he again showed his knack for working out of trouble by stranding runners at third base. Opponents are hitting .168 with runners in scoring position against him, the lowest average in the AL.
Notes
In his last four starts against Baltimore, Buchholz has allowed one earned run and 17 hits in 28 innings for a 0.32 ERA. … The Orioles are 29-17 with Buck Showalter as manager after going 32-73 under Dave Trembley and Juan Samuel. … For Boston, Adrian Beltre went 0-for-4 with three fly outs to right and a groundout to second, while J.D. Drew went 0-for-4 with three groundouts to second and a fly out to right. … Baltimore is 16-7 in its last 23 games overall and 9-8 against Boston this season. … Scutaro has reached base safely in 10 straight games.