Tom, earning his 15th cap and 'Pritch', winning cap number seven, were in the starting line-up at Oakwell while Harry had the honour of taking over the captain's armband for the final 20 minutes.
Alex was bright in the first half and Saido Berahino had a goal disallowed when he was flagged offside following in the midfielder's shot. The pair then combined again only for Vladislav Vasilyuchek to keep Berahino's effort out.
Vasilyuchek was there again to thwart the West Brom striker from Tom's assist and both Spurs men had efforts blocked as it stayed goalless going into half-time.
Harry entered the fray for his 11th cap just before the hour and had a couple of half-chances before Alex and Tom were replaced on 69 minutes.
Below: Harry takes over the captaincy
The Young Lions finally broke through on 83 minutes when Everton's Luke Garbutt whipped in a free-kick that was parried by Vasilyuchek and Middlesbrough's Ben Gibson slotted home the rebound.
Harry had one further shot wide and then set-up Danny Ings for an effort saved by Vasilyuchek as it ended 1-0.
Gareth Southgate's squad now travel to the Czech Republic for the UEFA U21 Finals.
England take on Portugal, France and Sweden in Group B and kick-off against Portugal on Thursday (June 18). Hosts Czech Republic are joined by Denmark, Germany and Serbia in Group A. The top two teams from each group go through to the semi-finals.