As one hit off David Price followed another and Yankees’ runners moved around bases like marbles set free in a bathtub, the architects understood how rare the scene was.

“It’s fun, you don’t see that very often,’’ Derek Jeter said of the first nine batters — one through nine in the order — getting a hit in the third inning Wednesday evening. “We were lucky, finding holes. That’s why you play the game. We were fortunate but we needed it.’’

The eight-run third off Price was the only frame the Yankees touched home plate but combined with another solid outing from Shane Greene it was more than enough to defeat the Tigers, 8-4, in front of a sold-out crowd of 40,876 at Comerica Park.

Jeter drove in two of the eight runs with a double and sacrifice fly and Jacob Ellsbury, Mark Teixeira, Carlos Beltran, Brian McCann, Brett Gardner and Francisco Cervelli also plated runs in the Yankees’ biggest inning of the season.

The last AL team to have nine straight batters get hits were the 1996 Tigers in Toronto. The Cardinals did it last year against the Pirates.