Lawes' Winnipeg rink downed Cathy Overton-Clapham's club 9-6 on Wednesday to improve to 2-0 in the third draw of the tournament.
The win ties Lawes with Stefanie Lawton's Saskatoon club at the top of the women's rankings. The Overton-Clapham rink is now 0-2.
"You can't complain when you start the first day of an event with two wins," said Lawes. "We're happy. I mean, we're still learning what the ice is doing and I think we're trying to manage it as best we can.
"It's a good first day for us."
Team Jones is being skipped by Lawes in place of Jennifer Jones, who gave birth to a baby girl two weeks ago. Jones is also recovering from knee surgery.
"It is a totally different lineup than our regular team," said Lawes. "I think we just have to take it as it comes and hopefully we can pick away at it."
Overton-Clapham's rink is also from Winnipeg.
Lawes scored four points in the fifth end to take a commanding 7-3 lead. They never looked back, adding points in the eighth and 10th ends.
"We're reading the ice well and we're within the tolerance of the shots and we're communicating well," said Lawes. "I think, also, our patience helps us.
"Hopefully we can take that forward."
Also in the third draw, Heather Nedohin's Sherwood Park, Alta., rink (1-1) topped Chelsea Carey's Winnipeg team 9-7, dropping Carey to 0-2.
The two wins give Lawton and Team Jones a good start on their quests for an Olympic berth in Sochi in 2014.
The winner of both the men's and women's tournaments will receive one of the six automatic qualification spots for the 2013 Roar of the Rings — the tournament that will determine who advances to the 2014 Winter Games in Sochi.
In men's action, Jeff Stoughton and Mike McEwen both improved their team's records to 2-0 in the third draw.
Stoughton's Winnipeg club beat Kevin Koe's Edmonton rink 7-5, while McEwen led his Brandon, Man., team to a 7-6 victory over Glenn Howard's crew from Coldwater, Ont.
Also, Kevin Martin from Edmonton, defeated Brad Gushue of St. John's, N.L., 10-7.
Koe and Martin are both at 1-1, while Gushue and Howard are 0-2.