The visitors came even closer on the quarter hour when Seb Carole saw his drive cannon off the underside of the Shels bar.
The opener finally came on 30 minutes when Blake found the net with another free kick.
Leeds had to wait until 13 minutes from time for their second, trialist midfielder David Prutton finishing from close range on his first appearance for the club.
Leeds included three Irish players in senior international Jonathon Douglas, who played in the centre of defence after the break, U-19 starlet Robert Bayly and centre half Graham Coughlan, who is on trial at Elland Road.
Shelbourne: Hussey, L'Estrange, McCulloch, Keely, Gartland, Roche, Chambers, O'Brien, Lacey, Leech, Quinn.
Leeds United: Gay, Bayly (Richardson), Marques (Heath), Coughlan (Douglas), Lewis (Boertien), Carole (Mullan), Fry (Thompson), Howson (Prutton), Westlake (Delph), Blake (Constantine), Elliott (Kandol).