JONATHAN Greening's second-half scorcher set Roberto Di Matteo on the way to his first win as Albion head coach at the Mestni Stadium.
The Baggies skipper smashed home a 25-yard beauty four minutes into the second half after the dangerous Luke Moore had opened the scoring in the ninth minute.
The Baggies were in control of this, their second pre-season friendly from start to finish and Jonas Olsson confirmed their supremacy by heading a third in the 73rd-minute.
Di Matteo started for the first time with new signing Simon Cox and Moore up front after the pair impressed at Histon.
There were also places for Greening - his first pre-season run-out - and young full-back Dwayne Samuels in the XI.
National skipper Robert Koren, Gianni Zuiverloon, Craig Beattie and Graham Dorrans all missed out through injury.
Albion were battling on two fronts from the first whistle, having to contend with their Slovenian First Division opponents AND the sweltering heat in the picturesque town of Lendava, which is renowned for its vineyards.
Albion, sporting their new red-and-blue away kit for the first time, sized up their opponents before drawing first blood in clinical fashion in the ninth minute.
The front two combined superbly, with Cox running at the NK Nafta defence before slipping in Moore, who calmly stroked the ball past keeper Ales Luk into the far bottom corner.
The hosts recorded their first shot of the game two minutes later but Konstantin Vassiljev was well off target from 25 yards.
With Youssouf Mulumbu impressing in his midfield anchor role, Albion looked bright in attack, with the lively Cox and Moore causing the Slovenian club's defence real problems.
And Moore had the ball in the net again on 17 when he converted Marek Cech's diagonal ball, but the effort was ruled out for offside.
Moments later, Chris Brunt cut inside from the right and tried his luck from distance, only to pull his left-footed effort harmlessly wide of the near post.
The Balkan outfit got behind the Baggies defence for the first time in the 21st minute when Bela Koplarovics broke down the left and pulled the ball back for Sinisa Jankovic, who shot horribly wide from 15 yards.
Albion had another scare on 27 when overlapping full-back Bojan Matjasec got to the right-hand byline and also found Jankovic, whose effort from just inside the box was much closer but failed to trouble Dean Kiely.
Some slick Albion interplay almost created a second goal on the half-hour mark.
Moore beat the offside trap to race onto Brunt's throughball before drawing Luk from his goal and squaring to Cech, whose back-flick attempt at the empty net was blocked in the six-yard box.
Albion were on top again but Cech was wayward with a speculative 30-yard effort.
The tourists almost added a second a minute before the break when Cox used his strength to hold off home skipper Damjan Oslaj before racing into the box and squaring to Moore.
The former Villa striker looked certain to score with just Luk to beat, only for Stepjan Caban to come out of nowhere and block his goalbound effort.
An ambitious 40-yard free-kick from Borut Gerencer, which drifted two yards over Kiely's goal, brought an encouraging Baggies half to a close.
Di Matteo rang five changes during the interval and switched to a 4-1-4-1 formation, with Cox, Brunt, Mulumbu, Abdoulaye Meite and Kiely making way for Do-heon Kim, Borja Valero, Joss Labadie, Shelton Martis and Luke Daniels.
It took Albion just four minutes to double their lead - and how.
Greening took a touch 25 yards out before smashing the ball into the top right-hand corner. Sub keeper Tomaz Murko got a hand to it but the shot was too powerful for him.
Albion continued to look comfortable and the head coach made his final three changes on 64, with David Worrall, Chris Wood and Filipe Teixeira coming on for goalscorers Greening and Moore plus Cech.
Murko had to contend with another ferocious strike from distance on 69 but managed to keep this one out, needing two hands to push away Labadie's right-foot rocket from a short Teixeira free-kick.
Wood should have been celebrating his first senior goal on 73 when Teixeira sent him clear of the NK Nafta defence, but the 17-year-old striker shot too close to Murko, who diverted his effort wide.
But it proved a momentary reprieve. From Teixeira's ensuring corner, Olsson stooped at the near post to head the ball into the bottom left-hand corner.
Daniels did not have a shot to save until nine minutes from time when he easily held onto sub Peter Gerencer's 30-yard grass-cutter.
However, Daniels was a little more concerned about sub Nejc Kolman's swerving drive, which crashed into his side-netting.
Teixeira should have made it 4-0 three minutes from time when he shot straight at Murko from 15 yards after being set up by Valero's sublime throughball.
NK NAFTA (4-3-3): Luk; Matjasec, Caban, Oslaj, Bunc; Mujakovic, B Gerencer, Vassiljev; Jankovic, Sebok, Koplarovics. Subs: Murko, Vinko, Kolman, Vas, P Gerencer, Miljkovic, Buzeti, Levacic, T Horvat, L Horvat, Bukovec.
ALBION (4-4-2): Kiely (Daniels HT); Barnett, Meite (Martis HT), Olsson, Samuels; Brunt (Valero HT), Greening (Worrall 64), Mulumbu (Labadie HT), Cech (Teixeira 64); Moore (Wood 64), Cox (Kim HT).
GOALS: ALBION - Moore (9), Greening (49), Olsson (73).
BOOKINGS: None.
REFEREE: B Mertik (Slovenia).
ALBION STARMAN: Luke Moore.
PIC: ON THE MARK...Moore is congratulated by Cech and Cox after his opening goal
