Air Force running back Asher Clark scores on a 23-yard touchdown run during the second quarter of the Falcons’ 35-34 victory over Navy. (Luis M. Alvarez/ASSOCIATED PRESS)

When the Air Force football team last was in the D.C. area, its opponent was Navy in what is annually the first leg of the Commander-in-Chief’s Trophy for both schools. The Falcons’ 35-34 overtime victory in Annapolis on Oct. 1 not only wound up as the closest game among the three service academies this year but also impacted postseason fortunes months later.

In the aftermath of that loss, the Midshipmen dropped four in a row, including two games by three points or fewer, during a six-game slide that was their longest since 2002. That stretch severely damaged Navy’s chances of reaching a ninth straight bowl game, forcing the Midshipmen to have to win out in order to qualify.

Air Force, meantime, improved to 3-1, and although they lost their next three, the Falcons closed by winning four of five to earn a school-record fifth consecutive bowl berth. Now they’ve come to the nation’s capital to play in the Military Bowl at RFK Stadium, taking one of the slots originally allocated for Navy.

The Midshipmen began the season with a tie-in to the Military Bowl, but bowl officials had to scramble to find a replacement once Navy was ensured a losing season on Nov. 19 following a 27-24 loss to San Jose State. At the time, Air Force needed to win one more game to become bowl eligible, and fortunately for Military Bowl officials, the Falcons had little trouble dispatching Colorado State a week later, 45-21.

Air Force (7-5), which faces Toledo on Wednesday, is the lone service academy playing in a bowl game after all three qualified together for the first time last year.

“I know [bowl officials] wanted Navy originally, but since they weren’t bowl eligible, it’s nice that they got another service academy to fill the slot in the Military Bowl,” Falcons senior quarterback Tim Jefferson said. “That’s pretty essential to the bowl game, having a military team in there.”

Jefferson was among the more significant players involved in Air Force’s narrow victory in Annapolis, scoring on a one-yard run in overtime to tie the game. Place kicker Parker Harrington then booted the extra point, and Falcons players stormed the field in one of the more improbable conclusions in the heated rivalry.

Moments earlier, Navy’s Kriss Proctor had scored the go-ahead touchdown on the first possession of overtime. The senior quarterback, however, was called for unsportsmanlike conduct stemming from an exchange of words with an Air Force defender, moving the extra point attempt back 15 yards. The Falcons blocked senior place kicker Jon Teague’s try after Navy had erased an 18-point fourth-quarter deficit.

Two years ago, Air Force was on the losing end in overtime, 16-13, at Navy-Marine Corps Memorial Stadium when place kicker Erik Soderberg missed a 31-yard field goal attempt wide left. The Midshipmen had taken the lead on Joe Buckley’s 38-yard field goal on Navy’s first possession of overtime.

Since then, Air Force has gone 5-0 against its fellow service academies and has won the Commander-in-Chief’s Trophy each of the past two seasons.

“We hope we can continue that tradition and keep it in Colorado,” said senior running back Asher Clark, who scored two touchdowns this year against Navy and added a 46-yard run.

Clark also is by far Air Force’s leader in rushing yards in bowl games among current players. He has 216 rushing yards in three postseason appearances, including a career-high 129 in a 47-20 win against Houston in the 2009 Armed Forces Bowl. Clark scored his only two bowl touchdowns in that game as well.

Jefferson has 452 yards combined passing and rushing in three bowl games.

“I think you need to realize it’s quite an achievement, an amazing achievement any time you get to play in a bowl game at a service academy,” Air Force Coach Troy Calhoun said. “There’ve been a good number of years where we didn’t play, and so you realize how unique and how awesome it is.”