Eric Gagne will team with lefty Hideki Okajima to make up a formidable relief combo for the eighth inning.

AP / Tony Gutierrez

BOSTON — A year ago, the New York Yankees made the deal the Red Sox wouldn’t — or couldn’t.

Yesterday, in a neat bit of symmetry, the situation was reversed.

Outbidding their longtime rivals — and at least two other teams — the Red Sox snared reliever Eric Gagne from the Texas Rangers, packaging three players for the two-month rental.

The Sox gave up pitcher Kason Gabbard, outfielder David Murphy and former Dominican bonus baby Engel Beltre for Gagne, who gives the Sox another closer option and depth in their bullpen.

Boston’s offer trumped that of the Yankees, who, according to sources familiar with the talks, were unyielding in their willingness to include any prospects who interested Texas.

Sources indicated that the Yankees wouldn’t include either outfielder Brett Gardner or right-handed pitcher Alan Horne in a deal for Gagne, leaving the door open for the Sox to make their pitch.

“I just assumed (Gagne) was going to go to the Yankees,” said an executive with another team yesterday. “They needed him the most.”

But the Yankees were as protective of their prospects yesterday as the Sox were last year, costing them the chance to land either Bobby Abreu and/or starter Cory Lidle.

(Strangely, given their bullpen needs, the Yanks subtracted rather than added yesterday, dealing off Scott Proctor for third baseman Wilson Betemit.)

Player cost aside, the deal was an expensive one for the Red Sox. In obtaining the 31-year-old Gagne, the Sox picked up the remainder of his $6-million base salary — approximately $2 million — and, in order to satisfy Gagne, threw in $2.1 million toward his incentive clauses.

Gagne had a limited no-trade clause in his contract with Texas, with a list of 12 teams to which he couldn’t refuse to be dealt. The Yankees and Mets were on that list, but the Sox weren’t, meaning they had to offer money to get him to agree to the deal.

In his deal with the Rangers, Gagne had performance bonuses for games finished. Since he won’t reach those with the Red Sox, Boston agreed to pay him $2.1 million of the $2.5 million he could have earned; the Rangers will pay Gagne the remaining $400,000.

Factor in the $650,000 the Sox paid to Beltre, only to trade him 13 months later while he was at the lowest rung of the organizational ladder, the out-of-pocket cost for the Sox is $4.75 million for two months’ worth of Gagne.

Still, the Sox were hardly complaining.

“We’re excited,” said general manager Theo Epstein. “We feel like we have a really good club, and we were looking to improve it. This helps give us what we think is a truly dominant bullpen. It was a lot to give up, but we certainly think the rewards justify it.”

Gagne, whom the Sox considered signing last winter before the base salary became too much of a risk given Gagne’s health — he’s had multiple elbow and back issues — can close games when Jonathan Papelbon isn’t available, and team with lefty Hideki Okajima to form what may be the most formidable eighth-inning combo in the American League.

“We now have three guys (at the back end of the bullpen) who we don’t have to match up,” said manager Terry Francona. “You just let them pitch good baseball.”

“Having another weapon,” added Epstein, “means you can plan properly and keep guys fresh.”

Having established several days ago that Gabbard would be part of the package for Gagne, the Sox reluctantly signaled a willingness to include Beltre on Monday. Yesterday, Murphy was added, trumping 11th-hour offers from the Mets and perhaps one other major-league team, believed to be the Chicago Cubs.

Gabbard boosted his value with his recent run of mostly strong starts in place of Curt Schilling, while Murphy, a former No. 1 pick from Baylor, gets a chance to jump-start a career after falling behind Pawtucket teammates Brandon Moss and Jacoby Ellsbury on the Sox’ outfield depth chart.

While the Sox bolstered their bullpen, they weren’t as successful in landing a right-handed bat to supplant Wily Mo Pena.

Jermaine Dye of the Chicago White Sox was their primary target, and after turning down Chicago’s demand of a package that included Pena and either Justin Masterson or Manny Delcarmen, the Sox offered Pena and Craig Hansen late Monday night.

But yesterday, according to major-league sources, the White Sox made their final proposal — they wanted two of the three pitchers discussed: Delcarmen, Masterson and Hansen. The Sox balked and the deal collapsed.

While players can still be traded through August, they must first clear waivers. Dye, several executives agreed yesterday, wouldn’t clear, especially to the Sox, who hold the best record in the American League. The waiver process works in reverse of the standings, meaning 12 other A.L. teams would have to pass on Dye for the Sox to revisit a deal for him.

Other less-glamorous upgrade possibilities remain, however, including Brady Clark, signed to a Triple A deal last week, and Bobby Kielty, who was designated for assignment by the Oakland A’s last week.

smcadam@projo.com