Koe's win set up a three-way tie for first at the Tim Hortons Brier, as John Morris of B.C. then beat Eddie MacKenzie of Prince Edward Island 10-4.
Morris, Koe and Stoughton are all tied at 4-1 at the top of the standings.
Koe grabbed a three in the third end and stole a crippling four in eight when Stoughton was forced into a low-percentage angle raise and his stone sailed past a crowded four-foot.
Stoughton shook hands at that point.
"We thought we had to give it a shot to score," he said.
"It was one of those games, we were just a little bit light or a little heavy on some shots. . . we missed four in a row on the end where they stole three."
Koe's four in eight came despite a hog-line violation on third Pat Simmons final stone.
"I think he said he thought he was coming out a bit light and went to add a little and you know just over the hog line," said Koe.
A missed raise by Manitoba's third that could have spilled Alberta stones out of the crowded four foot also put Manitoba further behind the eight ball.
"They kind of missed the sweep on John Mead's last shot and never moved stuff around and were chasing."
Stoughton noted the kind of shots he has been forced to make by his team have brought down his percentages but he feels good about his game.
"It's a reflection of lead, second and third before you," he said. "The less shots that are made in front of you, the tougher shots you are making. . ."
"I felt a lot better today about the ice and the weight and throwing, so for me the confidence level went way up after this game."
Newfoundland and Labrador's Brad Gushue improved to 2-3 with a 9-7 win over James Grattan of New Brunswick, who won his first game in the earlier draw. Northern Ontario improved to 2-3 by beating still winless Jamie Murphy of Nova Scotia 9-6.
Morris was happy about the way his team played.
"Jimmy was feeling it, the ice was fantastic . . . That was probably our most solid game of the week so far," said Morris.
Jim Cotter throws fourth stones for B.C. and he didn't miss much. P.E.I. shook after the final four in the ninth end.
Earlier in the day, Koe won a game he never looks forward to playing.
"This one, you don't get a lot of enjoyment out of," the Alberta skip said, after beating younger brother Jamie Koe from the Northwest Territories-Yukon 8-3 in eight ends.
"It's never fun beating them because I'm always cheering for them every year they're here," he said. "That being said, we needed a win."
"They're obviously better," Jamie said of the encounters with his brother. "We're going to have to play our best and hope for some breaks but it's a fair battle."
Monday also saw Grattan score his first against Greg Balsdon of Ontario 9-6 in the afternoon. Balsdon now sits at 2-2.
Grattan gave Stoughton a fight Sunday as well and said it felt good to get a monkey off his back with the win.
"When we went to bed last night we felt pretty good about it," he said of the Manitoba game. "The team in the last two games has really shown up."
He says getting used to the ice has been an issue. They lost their first game 13-5 and the second 10-1.
"We come from an area of the world where the ice is fairly straight all the time . . Coming out here and all of a sudden you're taking the 12-foot to get to the lid and it's a different ball game."
It's also important to win games at the Brier if you want a reserved spot in the future. A new system is coming into place that will force the bottom finishers to compete for the right to return.
It's being brought in to keep the field the same size with the addition of a Team Canada and new rinks from Nunavut and Yukon, instead of just one Territories team.
MacKenzie was 3-2 after splitting the day with an afternoon win over Quebec's Jean-Michel Menard.
MacKenzie has already matched his combined record at his first two Brier appearances for Prince Edward Island, in 2011 and 2013.
"It's definitely better than 0-5 or 0-6 like we were the last couple of times," he said earlier in the day.
"I'd say being here the last three out of four years helps for sure, playing on arena ice a little more."
Saskatchewan's Steve Laycock sits just ahead of MacKenzie at 3-1, after beating Nova Scotia 5-3 in the afternoon. He didn't play Monday night.
"We kind of figured 3-1 or 4-0 was where we'd want to be after this stretch because we do have some of the favourites coming up," he said.
Murphy, meanwhile, isn't too thrilled at the Canadian Curling Association for the changes coming in 2015 that could see Nova Scotia have to compete for the right to play in the Brier.
"We're firm believers that messing with traditions such as the Brier doesn't seem like a smart decision," he said of the new system, popularly known as relegation, although it seems anything but popular.
"We're obviously biased when we say that because we're probably going to be in the relegation pool."