Georgetown withstood a remarkable comeback by American University and defeated the Eagles, 71-69, last night in the opening game of the Hoya Invitational women's college basketball tournament at McDonough Arena.

In tonight's 8 o'clock championship game, the Hoyas (7-4) play Fairleigh Dickinson, a 78-77 winner over Boston University in last night's second game.

The Hoyas seemed to have last night's game well in hand when they outscored the Eagles, 10-2, at the start of the second half and took a 41-23 lead with 17:30 remaining.

But the Eagles (6-5) refused to fold and Georgetown lost its shooting touch after making its first seven shots of the half. AU chipped at the Hoyas and went up by four point, 61-57, on two free throws by freshman Darsi Smith with 5:08 to play.

That is when the Hoyas steadied themselves. K. C. Comerford hit two straight jumpers to tie the game, and Kit Hepp made two free throws with 3:52 left to give Georgetown a 63-61 lead. The Eagles were within two, 71-69, with 31 seconds to play but missed two shots, the last an eightfooter by Smith with three seconds to go.

Smith, who had 10 rebounds, and Georgetown's Abbie Dillon each scored 20 points. Ulrika Myhr had 14 points and 14 rebounds for the Hoyas. There were more fouls than baskets as the Hoyas had four players foul out and the Eagles three.

Despite the victory, Georgetown Coach Frank Carr wasn't happy. "We've never played that badly," he said. "We fooled around and never went through our plays. We were lucky to get out alive."