BRISTOL, Conn. — Falmouth Little League Manager Matt Rogers was going to be a little light in the wallet after happily delivering on a promise.

“I’m going to the Slurpee machine, times 12,” Rogers said after Falmouth scored six runs in the top of sixth inning Tuesday to defeat Barnstable, Massachusetts, 9-4 to stay alive in the New England Regionals at Breen Field.

Falmouth sent 10 batters to the plate in the inning, meaning all the players could look forward to the slushy delight because Rogers treats any time his team bats around.

Brady Douglas, who turned 13 on Monday, gave himself a belated birthday present by snapping a 3-3 tie with a two-run single that started the scoring in the sixth and turned out to be the winning hit.

“I’ve been struggling at the plate lately,” Douglas said. “I really wanted to step up for our team. It just felt great to get that hit and drive in some runs.”

Joshua LeFevre’s infield single made it 6-3 and Michael Simonds broke it open with a three-run home run over the left-center-field fence.

Falmouth, hoping to advance to Thursday’s semifinals, became the first team from Maine to finish 2-2 in pool play since Portland North in 2007.

Falmouth won’t know its fate until after Wednesday’s final round-robin games: Williston, Vermont (1-2) vs. Cumberland, Rhode Island (2-1) and Barnstable (1-2) vs. Goffstown, New Hampshire (1-2).

If Goffstown and Williston win, they could oust Falmouth in a three-way tie based on the fewest runs allowed tiebreaker. Goffstown has allowed 15 runs, Williston 20 and Falmouth 26.

“We’re rooting for all the teams to play well,” Rogers said. “They’re all kids. You don’t root against anybody.”

Falmouth won’t worry about the tiebreaker as it has a trip planned for Wednesday to Lake Compounce, a nearby amusement park.

“I was praying we would win today because hopefully we advance now,” Douglas said. “It’s the best thing you could ask for.

“We’re in Bristol, our regionals, having the best time of our lives.”

Alex Smith earned the win, allowing four runs – but only three hits – over 51/3 innings with a walk and four strikeouts.

He said Douglas’ hit was like a weight being lifted from his shoulders.

“I was screaming and jumping up and down when Brady got that hit,” Smith said. “I have a little room to breathe when I get out to the mound the next inning.”

Falmouth grabbed a 1-0 lead in the top of the first on a double by Francis Kiely, who was 3 for-4, and Sam Manganello’s groundout.

Barnstable took a 2-1 lead on Nick Locasio’s two-run double in the second and Falmouth failed to score in the third after loading the bases with no outs.

Falmouth loaded the bases again in the fourth and got a break when Douglas’ line drive couldn’t be handled by left fielder Colby Burke, allowing two runs to score.

Barnstable tied the game in the bottom of the fifth on Burke’s sacrifice fly.

Held to seven runs in its first three games, Falmouth waited until the final inning Tuesday to finally break out offensively.

“We’ve been frustrated because we feel like we can hit and we just haven’t done it,” Rogers said. “We did it today.

“I told them I didn’t get any hits. It’s all them. These guys are great players and great kids. I’m just so happy for them to do it today.”