The youngster, who came on as a sub for defender Steve McKeown on half-time, could have had a sensational hat-trick but he had a penalty saved by 16-year-old Albion keeper John Bateman on 80 minutes.
The deadlock was broken after only a quarter of an hour when Nick Gray put Leeds in front following good work from Joel Griffiths and a flick-on by Eirik Bakke.
The Baggies equalised quickly when teenage striker Stuart Nicholson hit the back of the net with a drive that gave Mark Wilberforce no chance in the Leeds goal.
Bakke made an impression in midfield and it will be interesting to see if he features against Plymouth at the weekend.
18-year-old Howson scored his first and Leeds' second when he caught Bateman off his line and lobbed him from a distance.
Then he latched onto Griffith's through ball and hit a drive past the keeper to make it 3-1.
Griffiths was then brought down for the missed penalty ten minutes from time.
Leeds reserves have now picked up 18 points from their last eight games.
United: Wilberforce, McKeown (Howson h/t), Harding, Hird, Walton, Bakke, Griffiths, Gray, Moore (Ameobi 83), Parker (Bayly 57), Pugh.
Subs Unused: Camfield, Hutton.
Albion: Bateman, Hodgkiss, McMenamin (Darg 83), Davies, Baker, Forsyth, Kelleher (McQuilken 28), McGovern (Downing 75), Elvins, S Nicholson, Pringle.
Subs Unused: D Nicholson, McDonald.