Brogan Hay gave Malky Thomson’s side the lead inside the opening 20 minutes before a Pernille Harder double had Chelsea ahead at the break.
Bethany England and Emma Thompson added to the scoring in the second-half.
Jenna Fife started in goal with Sam Kerr slotting in at right-back. She was joined in the back four with Chantelle Swaby, Brianna Westrup and Nicola Docherty.
Chelsea Cornet, Tessel Middag and Lizzie Arnot made up the midfield three with Brogan Hay and Jane Ross supporting striker Kayla McCoy.
Megan Cunningham, Demi Vance, Kirsten Reilly and Zoe Ness were joined on the bench by six Academy players, Emma Watson, Jodi McLeary, Kirsty Maclean, Hannah Jordan, Kayla Jardine and Eilidh Austin.
Lizzie Arnot tested the Chelsea goalkeeper inside the opening few minutes as she swung a left-footed free-kick towards goal which was tipped over the bar by Ann-Katrin Berger.
Erin Cuthbert had a shot wide for the visitors in a lively start to the match before Drew Spence rattled the crossbar with a powerful effort from inside the box.
In the 17th minute, Chelsea continued to push for the opening goal as Guro Reiten’s cross was met by Erin Cuthbert but her header was just wide of Jenna Fife’s goal.
It was Rangers who took the lead in the 19th minute as Brogan Hay was quick to react to a loose ball from the Chelsea defence. Hay’s initial shot was pushed away by Berger but landed back at the Gers winger who made no mistake in slotting into the back of the net.
However, the 2020/21 Champions League finalists were back level after only one minute as Guro Reiten’s cross was headed home by Pernille Harder.
The visitors were awarded a penalty on the 28th minute as the referee judged the ball to have bounced off the hand of Rangers captain Brianna Westrup inside the box. Harder stepped-up to the spot and fired Chelsea into the lead with her right-footed penalty.
Bethany England was next to threaten for Emma Hayes’ side but her shot was blocked well by Jenna Fife.
Into the second-half, Erin Cuthbert threatened again as Chelsea looked to increase their lead. The former Rangers Girls’ Academy player got a shot away from the edge of the box which bounced back off the post before being cleared.
Fife pulled off a fantastic save as she denied a curling effort from Pernille Harder pushing it wide for a corner. The Gers number had a busy start to the second-half as she blocked a Bethany England shot shortly after as Chelsea looked to increase their lead.
Rangers broke in the 65th minute as Nicola Docherty picked out Sam Kerr in midfield and she showed her pace to drive down the left-hand side and fired a shot across goal but it was just wide of the post.
Chelsea made it three with 20 minutes of the game remaining as Erin Cuthbert delivered a ball across the face of goal and Bethany England tapped home from close range.
Substitute Emma Thompson made it four for Chelsea as she shot from the edge of the box with her low effort beating Jenna Fife.
Gers’ attention now turns to Sunday’s SWPL Cup group match against Motherwell.
RANGERS: Fife, Kerr (Jordan, 89), Swaby (Watson, 88), Westrup (Jardine, 89), Docherty, Cornet (Austin, 89), Middag (Vance, 70), Arnot (Reilly, 70), Hay (Maclean, 88), Ross (McLeary, 81), McCoy (Ness, 46).
SUBS: Cunningham.
CHELSEA: Berger, Carter, Leupolz (Guyatt, 74), So-Yun (Thompson, 74), Reiten, Cuthbert, Spence, Wardlaw, England, Harder, Fox (Beever-Jones, 74).
SUBS: Darey.