Graham received Ripley Nielsen's pass from 10 yards out in the slot and fired the game-winning goal past Ian Allender with 1:23 remaining in the first extra session. Tower Hill started the season with two losses in its first three games and has now won five straight to boost its record to 6-2.
"That spot in the slot about 10 yards out was open all day," said Graham, a junior midfielder. "We were unlucky several times with balls bouncing off posts. I got the ball in good position and that was the game. It feels amazing."
Nielsen sent the game into overtime with a difficult wraparound goal with 1:24 left in the fourth quarter. He faked one way and reached around Allender to even the game at 6.
"Knocking off Archmere, a team that was undefeated, is huge," said Nielsen, who had two goals and one assist. "In overtime, I fed Jake and he made an amazing shot."
Chas Robino also scored twice for the Hillers.
The teams went back and forth all day and finished with the same number of shots -- 29.
Both goalies -- Allender (five saves) and Tower Hill's DeMetrius Murray (14 saves) made their share of big plays.
"Anything could have happened in this game," Archmere coach Noel Breger said. "It was one of those things. Both teams played great. In overtime, our ball bounced the wrong way and theirs went in. It easily could have gone either way."
Phil Pieretti scored three goals for the Auks while Jim Bowers added one goal and two assists.
The Auks went ahead 6-5 with 3:49 left in regulation when Bowers fed sophomore Chris Thomson after the ball was knocked out of Murray's stick.
"I'm very proud of my team," Breger said. "We have a very good team and we're very young. We have a lot of freshmen and sophomores who continue to improve."
Tower Hill has been one of the most improved teams in the state during its five-game winning streak.
"We fell behind late in the game and showed a lot of character," Tower Hill coach Brad du Pont said. "My team is really growing up. I think we're getting better. We play a hard schedule and I think it makes you tougher as the season goes on."
Tower Hill 0 2 2 2 1-7
Archmere 0 2 1 3 0-6Goals-TH: Robino 2, Nielsen 2, DeDominicis, Timmons, Graham; A: Pieretti 3, Freeborn, Bowers, Thomson. Assists-TH: Nielsen; A: Bowers 2, Thomson, Segrin. Shots-TH 29, A 29. Saves-TH 14 (Murray), A 5 (Allender).