Hill allowed just one run on three hits in 5 2/3 innings and struck out seven. The game ended in seven innings due to the 10-run rule as Canada's bats woke up late.
"They were pretty patient. I just attacked them with fastballs," said Hill, who went 9-18 in six years with the Montreal Expos, Washington Nationals and Toronto Blue Jays.
"They held us in check a long time," said Canada manager Ernie Whitt. "We got some big hits, and luckily we had a guy [Hill] who shut them down.
"We were just trying to get some runs. If you're only one or two hits from them getting back into it, it's nerve-racking. We would rather play as underdogs instead of favorites. Any team can beat you."
Canada will next face the winner of Friday's game between Germany and the Czech Republic, while Great Britain will take on the loser. Both of those games will be on Saturday.
Before a crowd of 3,704 fans, Canada jumped on the board in the first inning with two unearned runs due to poor execution by the British team. After a walk, Chris Robinson advanced to third on an error by British third baseman Mike Johnson, who mishandled Tim Smith's single to left field. Left fielder BJ Hubbert's throw to third appeared to be in time but Johnson did not field it cleanly.
"I was a little too aggressive," said Robinson. "It's one of those, 'Oh, a great play, don't ever do it again.' It was a good call. He did miss me. "I thought I was fast."
Robinson then scored on a wild pitch by Britain starter Chris Reed. Smith then crossed the plate on Jimmy Van Ostrand's groundout to third for a 2-0 Canadian advantage. Canada had a chance to pull away in the fourth, loading the bases with a hit, error and walk, but Tyson Gillies struck out to end the rally.
Canada got their two-out run an inning later with Adam Loewen delivering a double down the right-field line to score Van Ostrand from first base, pushing the lead to 3-0.
Hill was cruising through the British lineup, not allowing a hit out of the infield until Johnson's hard single back up the middle with one out in the fifth.
With Hill approaching the World Baseball Classic-mandated pitch limit of 85 pitches, Great Britain tallied their first run in the sixth inning when Albert Cartwright belted a home run just inside the left-field foul pole to cut the deficit to 3-1.
"It was just a really bad slider. I had made some bad sliders and I tried to make an adjustment. But you still have to give the other guy credit," said Hill.
With one out in the seventh inning, Sam Wiley lined a ball to the wall in right field, but the British DH decided against testing Loewen's arm and going for a double. The next batter, Chris Falls, grounded into a double play.
Canada broke open the game in the bottom of the seventh with eight runs. Gillies doubled to start the inning and scored on Robinson's single to left -- which came after he fought off a number of pitches. Van Ostrand crushed a two-run home run to right-center field for a 6-1 lead.
Next, Skyler Stromsmoe emptied the bases with a three-run double to right center and Gillies ended the game with a triple to score Stromsmoe and Jonathan Malo.
David Hein is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.