Rowen Powell, Ben Newton and Stevenson then all kicked two goals apiece too for Subiaco.
It was Subiaco captain Kyal Horsley who was clear best afield, though, as he continued his dominant start to the 2018 season with 40 possessions, five marks and five inside-50 entries through the middle for the Lions.
Leigh Kitchin was also impressive on the ball ending the afternoon with 27 disposals and a goal with Chris Phelan collecting another 25 touches, Craig Hoskins 21, Jacob Miller 21 and Newton 20 along with his two goals.
Subiaco had its hands full with West Perth's forwards but got better the longer the game went both defensively and with repelling attacks and setting up play from the back half.
Hayden Kennedy led the way with that with the premiership small defender amassing 26 possessions and nine marks with Greg Clark adding 24 disposals and five tackles, and Angus Litherland 18 touches and six marks.
Subiaco's big men made good contributions too with Zac Clarke finishing with 16 possessions, seven marks and 33 hit outs, and Lachlan Delahunty 17 disposals, six marks, 14 hit outs and a goal.
Tyler Keitel kicked two goals in attack for West Perth in the first half and ended the day with 15 possessions and six marks, but he would have been disappointed with two missed gettable shots in the second half.
Michael Lourey once again had to fight above his weight division in the ruck after Chris Keunen went down injured early. Following a strong showing against Perth last week, Lourey battled hard against Zac Clarke and Lachlan Delahunty. He had 11 touches, seven marks and eight hit outs.
West Perth's midfield had plenty of impressive ball winners led by captain Aaron Black who amassed 36 possessions, nine marks and seven tackles.
Shane Nelson compiled another 29 disposals, Corey Chalmers 26, Luke Meadows 25, Trent Manzone 22 and Blake Wilhelm 22.
Steve Potente came in to play his first game of the season and brought up his 100th appearance in the WAFL in the process. The 2013 premiership winning small forward played well too with 20 possessions and a goal.
Andrew Strijk also had 20 touches, nine marks, seven inside 50s and a goal for West Perth.
The West Perth back-line held up well also led by Jordan Mills who continues to be rewarded for his dedication at reserves level by now cementing himself in the Falcons' league side.
West Perth's stunning start continued with Nathan Alexandre and Trent Manzone also kicking truly while Subiaco went goalless until Brad Stevenson goaled at the 24-mintue mark. But the Falcons had still done a tremendous job to lead by 10 points at the first change.
The Lions did kick a goal early in the second term through Rowen Powell in less than a minute but West Perth again steadied. That was firstly thanks to a goal to Steve Potente in his 100th game while Keitel's second soon after put the Falcons back out to a 15-point advantage.
Kyle Halligan's first goal of the day got one back for Subiaco but West Perth retained its advantage with the response from Keegan Knott to still be 14 points in front at the 23-minute mark.
But the Lions finished the first half strongly with goals to Leigh Kitchin, Lachlan Delahunty and then Halligan as they took their first lead of the game to be three points to the good at the main break.
The Lions lead grew to nine points to start the third quarter with a goal to Halligan but the Falcons pulled that back to three soon after when Andrew Strijk kicked truly.
Subiaco took control from there, though, with West Perth going more than 30 minutes of game time without another goal.
In the meantime, the Lions scored through Ben Newton, Daniel Perkins, Newton again, Halligan with his fourth and then Stevenson his second to be 32 points by six minutes into the last quarter.
West Perth got back within 19 points with a couple of consecutive goals to Rudy Riddoch and Jay van Berlo, but the Lions did enough to remain undefeated in 2018 and come away with the hard fought 22-point victory.
West Perth's reserves delivered another impressive performance on Saturday at Leederville Oval to beat Subiaco 13.12 (90) to 10.5 (65).
The Falcons trailed by 13 points at quarter-time, five points at half-time and 10 points at three quarter-time, but finished strongly with six goals to one in the last term to win by 25 points.
Brayden Antonio kicked three goals to go with 21 possessions and five tackles for West Perth with Mitch Antonio, Baylee James, Dylan Yem and Daniel Del Prete kicking two goals apiece.
Mitch Peirce amassed another 30 possessions for the Falcons reserves, Alex Coe 20, Kael Coleman 19, Matt Guadagnin 18 and Conal Lynch 16.
Sean Bradley, Shannon Nelson, Daniel Leach and Tom Edwards-Baldwin all kicked two goals apiece for Subiaco.
Leach also picked up 30 disposals for the Lions with Braden Fimmano finishing with 28 touches, Ben Reid 20, Scott Hancock 19, Mckenzie Lawrence 19, Nelson 18 and Ryan Wade 17.