City have 19 points from seven games ahead of second-placed Chelsea, who are on 15 points but with two matches in hand before they visit sixth-placed Liverpool on Sunday.
Shaw netted 23 seconds after kick-off at Etihad Stadium when she pounced on an error by Australian centre-back Clare Hunt.
"We really enjoyed that one," Shaw told Sky Sports. "We spoke as a team about wanting to come out here and be on the front foot.
"We said we hadn't really scored early in a game, so we're going to go and press, and it worked out."
The Jamaican continued to cause nightmares for Hunt, getting her second goal in the 15th when she nodded home Lauren Hemp's pinpoint cross, the first of three assists for Hemp.
Jill Roord scored for the third successive WSL game to give City a three-goal lead in the 66th minute with a blistering left-foot shot before Shaw completed her hat-trick a minute later, tapping in Hemp's low cross from the far post.
"With the players I have around me, I know I'm going to get crosses, and just making the right movement in the box they'll find me," Shaw said.
"It's something I pride myself in, especially being in the box and the ball being out wide, I know I have to be ready for the crosses."
Shaw, who has three trebles against Spurs, stretched her lead atop this season's WSL scoring charts as she moved onto seven goals, and her six career hat-tricks also lead the WSL.
"I feel like I always know where Bunny (Shaw) is going to be, I know where she's going to run, especially for that third goal, I just thought I'd put it into space and obviously Bunny was there to finish it," Hemp said.
Hemp had a couple of terrific chances herself, forcing goalkeeper Rebecca Spencer to make a diving save from one shot, and then firing another soon after that ricocheted off both posts and out. Hemp buried her head in her hands in disbelief.
"I was absolutely devastated," the England forward said.
The defeat leaves Spurs, who substituted Hunt and also brought on fellow Matildas star Hayley Raso, in seventh spot on seven points.
City, who fielded Alanna Kennedy at the heart of their defence, also brought on fellow Matilda Mary Fowler, but she was not required on the goalscorers sheet.Â
Matildas striker Caitlin Foord (l) was on target in Arsenal's 5-0 hammering of Brighton in the WSL. (AP PHOTO)
At the Emirates Stadium in London, Arsenal registered a 5-0 thumping of Brighton & Hove Albion to close the gap on the visitors who remained third on 13 points.
Manchester United, who have two games in hand, can go third with a home win over Aston Villa on Sunday.
Beth Mead, Caitlin Foord, Frida Maanum, Lina Hurtig and Alessia Russo, with a penalty, secured Arsenal's third win.
The Gunners also brought on 22-year-old Matilda Kyra Cooney-Cross, as they moved to fourth on the table, just one point adrift of Brighton.
Brighton had only conceded four goals in their first six games this season before Friday's nightmare at the Emirates.
