The Sky Blues were down by three goals to their English opponents but strikes from Renee Rollason and Jodie Taylor in a six-minute spell late in the second half gave them hope of an upset.
The game could easily have had a different ending after Sydney dominated the early part of the match, with forwards Taylor and Leena Khamis having chances to open the scoring, while a Sam Kerr header hit the crossbar close to half time.
Coach Alen Stajcic kept an unchanged starting line-up to the one that won the opening game of the tournament 1-0 against NTV Beleza.
The Sky Blues were the first to go close when dual international Ellyse Perry delivered a cross from the right to the head of Taylor, who put her effort just past the post in the sixth minute.
Keeper Casey Dumont was called into action three minutes later to save from a Chelsea attack before Sydney had the best chance of the opening period on 20 minutes.
The Blues keeper Hourihan saved a header and the ball fell to Leena Khamis but the seasoned Matildas star could only send her shot over the bar.
A saving tackle from United States international Allie Long on the half hour prevented another Sydney scoring opportunity and the Sky Blues were made to pay moments later when Chelsea took the lead.
A passing move saw Rosella Ayane work the ball square to Laura Coombs who struck the ball hard and low beyond Dumont on 36 minutes.
Sydney went close to levelling four minutes later when Kerr hit the bar with a header and Chelsea were able to clear the danger to go in at the break 1-0 up.
The English FA Super League side took the ascendancy immediately in the second half. A free-kick from Japanese World Cup winner Yuki Ogimi came back off the bar, eventually falling to England international Eniola Aluko who smashed the ball home from 18 metres with 52 minutes gone to make it 2-0.
It was 3-0 five minutes later when a through ball from Rachel Williams split the Sydney defence, Ogimi raced on to it, rounded the keeper and slotted home.
The Sky Blues weren’t finished however and set up a grandstand finish.
Stajcic’s team won a free kick outside the box and Rollason fired in off the post to pull one back with 15 minutes to go.
The goal buoyed Sydney and it won another free-kick, this time an indirect one inside the box, from which striker Taylor stepped up and sent a delicate chip over the Chelsea keeper Hourihan and into the net with 81 minutes on the clock.
Sydney's brave effort was to no avail however and Chelsea was able to hang on and claim a place in the final on Sunday against Japanese champion INAC Kobe Leonessa, which defeated Chile’s Colo Colo 3-0 in the other semi-final.
The Sky Blues will remain in Japan to face Colo Colo for third place in a game which takes place on Saturday afternoon in Kagoshima.