Despite being up against a Baggies side that included many experienced first team players, United dominated the first half and raced into a two-nil lead with goals from Simon Johnson and Nicky Barmby.
Johnson's goal on ten minutes was special; he picked the ball up 30-yards out, cut inside and unleashed a curling shot that bent into the far corner of the net.
Playing the better football it was no surprise when Leeds extended their lead five minutes later. A cross from the left took a deflection in the box and Barmby was there to slide the ball home from ten yards out.
West Brom got themselves back into it before the break with a penalty that was hotly disputed by United, with some justification as it appeared that firstly Frazer Richardson got to the ball first and secondly the incident took place just outside the box. Either way the referee awarded the spot-kick and Martyn was beaten by Jason Roberts.
James Milner was left disappointed in the second half when his strike was chalked off for offside, the referee having given the goal at first but then seen the linesman's flag.
Leeds still put in a performance that was good enough for the three points and provided an excellent start to the season for Agnew's men.
"It was a really pleasing performance," said Steve, "We worked hard and had a good attitude in the game, and they got their reward.
"We played a really slick first 30 minutes where we had the majority of possession and were a real threat.
"The second half we weren't as effective in our possession and our passing wasn't as sharp, but we still caused problems for what was a very experienced West Brom side with the likes of Jason Roberts and Phil Gilchrist in it."
So far Steve has guided the second string on an unbeaten run lasting four games in which some of the club's younger players, such as James Milner and Aaron Lennon, have really flourished. It's been a satisfying start to his coaching career at Elland Road.
"I've really been enjoying the response from the players, they've made the job more enjoyable and I can see there's a lot more to come from these youngsters yet.
"We'll work with them more on the training ground and hopefully we'll develop them into excellent young players," added Steve.
United: Martyn, Krief, Richardson, Kilgallon, McDaid, Milner (Woods 65), McPhail, Barmby, McMaster, Simon Johnson, Lennon. Subs: Shields, Allaway, Constable, Armstrong.
Albion: Crane, Adams (Holmes 74), Gilchrist, Mkandawire, Midworth, A Chambers, Wallwork, Marshall, Dyer, Patterson (Clarke 74), Roberts. Subs: Warmer, Jones, Tomlinson.
Bookings: Mkandawire foul 86 (Albion).
Kilgallon foul 59 & McDaid dissent 83 (Leeds).
Ref: D Whitestone.