Stevens (19), also a former Green Island striker, scored twice from the spot and once in general play as the Wellington Phoenix reserve side edged Southern United 4-3 at Rugby Park.
Down 4-2 late, Tom Jackson gave the home side a glimmer of hope when he scored off his head in the 88th minute, but his side ran out of time and was left ruing missed opportunities and conceding a couple of penalties.
Playing into a strong first-half breeze in wet conditions, Southern missed a couple of early chances with captain Victor da Costa hitting the woodwork twice in the first five minutes.
Phoenix goalkeeper Oliver Sail was then forced into a couple of sharp saves as the home side strung a few more chances together.
However, Nathanial Hailemariam put the visitors up 1-0 against the run of play when Stevens found some space down the right hand flank and fired in a cross for the striker to latch on to in the seventh minute.
Jackson tied up the game in the 16th minute when he turned a loose ball into the back of the net from a corner, his first goal of Southern United's campaign. Da Costa and Jackson both came close to putting the home side up after the half-hour mark but could not find the back of the net.
Nicholas Hindson made no mistake shortly afterwards, though, taking a Jackson pass and rounding the keeper before sending the ball into the back of the net from a difficult angle.
The Phoenix quickly hit back through its first penalty after Southern United was called for a hand ball in the box.
Stevens calmly converted the penalty to knot the game up at 2-2 at the break, despite his team spending the majority of the first half defending.
The former Dunedin player scored the go-ahead goal for the Phoenix after 57 minutes, before adding his third from the spot in the 79th minute.
The home side welcomed Tom Connor back from injury, with the midfielder making his first appearance since injuring his hamstring against Canterbury United earlier in the month; yesterday he played the final 30 minutes off the bench.
Next weekend Southern United is on the road against Team Wellington,
the side which shocked league leaders Auckland City 4-0 on Saturday.
A goal in each half to Michael Gwyther and second half strikes from Luis Corrales and Jarrod Smith condemned Auckland City to its worst defeat in the ASB Premiership.
In the weekend's other two games, Waitakere United and Hawkes Bay United drew 1-1 in Whenuapai, and Wanderers SC beat Canterbury United 3-1 in Auckland to pick up its first competition points.
The Southern United youth team lost 2-1 to the Nelson Marlborough Falcons in Nelson yesterday.
By Robert van Royen.
ASB Premiership
The scores
Wellington Phoenix reserves 4
Joel Stevens 3, Nathanial Hailemariam
Southern United 3
Tom Jackson 2, Nicholas Hindson
Halftime: 2-2
