New York, which scored just 17 runs in its first six games, finished with season highs for runs and hits with 11.
Mussina earned win No. 251 and is tied with Gibson for 42nd place. He struck out three to equal Yankees TV broadcaster David Cone for 21st place with 2,668 Ks.
Jonny Gomes homered for the Rays, who are 3-3 heading into their home opener against Seattle on Tuesday. Tampa Bay has never finished with a winning record on its first road trip of the year.
The Yankees went 4-3 on their season-opening homestand and play 18 of their next 20 on the road. They were scheduled to fly to Kansas City after the game for the Royals' home opener Tuesday afternoon.
Joe Girardi may have a thin bench to work with as he starts his first trip as Yankees manager.
New York was without two regulars against the Rays and Jeter left before the third with a strained left quadriceps. First baseman Jason Giambi missed his second straight game with a sore left groin and catcher Jorge Posada got the day off.
Jeter beat out a potential double-play grounder after Johnny Damon led off the first with a single to left. Abreu then pulled a 3-1 pitch from Jason Hammel (0-1) over the wall in right to give New York a 2-0 lead on another chilly night in the Bronx.
The Yankees pushed across two more runs in the sixth. Abreu led off with a triple to right-center and scored on Alex Rodriguez's single. Matsui then doubled down the first-base line to drive in A-Rod and make it 4-1.
That was enough for Mussina (1-1), who allowed two hits and walked one. He improved to 8-1 with a 1.92 ERA in nine career starts against Tampa Bay at Yankee Stadium.
Brian Bruney, Kyle Farnsworth and LaTroy Hawkins each pitched a scoreless inning to finish off the three-hitter.
Hammel allowed eight hits and four runs in six innings. He struck out two and walked one.