The win makes Homan's Ottawa rink the only undefeated foursome in both the women's and men's draws.
Homan had an early 3-1 lead and was up 5-2 after stealing one in the sixth but gave up a deuces to Sweeting in the eighth and 10th. Homan had to draw the four-foot in the 11th for the win.
"I knew the path and knew the weight and had the sweepers to get it there," Homan said of the final shot.
"A great game for the fans. A ton of made shots from both teams. We had to fight for every point. They played a great game and we had to play our best to win. 4-0 is definitely a good position but we want to finish strong though."
Edmonton's Sweeting is 2-2. She beat Olympic champion Jennifer Jones of Winnipeg, 10-8 in Draw 5 earlier in the day.
In the morning draw, Homan drew to the button with her final stone to score one and beat Edmonton's Heather Nedohin 5-4. Nedohin now sits at 3-1 after downing Sherry Anderson (2-2), 7-4 in the late draw.
Jones made a raised takeout for five in the ninth end in a 12-7 victory over Sherry Middaugh (1-3) of Coldwater, Ont., in Draw 4.
Meanwhile on the men's side, Glenn Howard (3-1) of Penetanguishene, Ont., lost his first match of the tournament, 7-4 to Olympic champion Brad Jacobs (2-2) of Sault Ste. Marie, Ont., in Draw 6.
Jacobs scored two in the sixth end and added singles in the seventh and eighth to pull away with the victory. It was Jacobs' first win of the day after falling to Brad Gushue (2-2) of St. John's, N.L., 5-4 in the afternoon.
Howard started his day with a 4-3 win over Winnipeg's Mike McEwen (3-1) in Draw 5. McEwen took a 9-4 win over Jim Cotter (1-3) of Vernon, B.C., in the morning.
In other action from Draw 6, Calgary's Kevin Koe improved to 2-2 with a 8-7 win over Canada (1-3), which is skipped by Calgary's John Morris. Koe scored a single in the 11th end to seal the victory. On the women's side, Middaugh of Coldwater, Ont., scored two in the 10th end to edge Alison Flaxey (0-4) of Listowel, Ont., 8-7.
Round-robin play continues Friday with Draws 7, 8 and 9.