The reserves gave an impressive performance with Blake, Jermaine Beckford, Rui Marques and Ian Westlake also included in a side which mixed youth with experience.
Beckford who had the first opportunity of the night, chipping over the bar after only 10 minutes, before 16-year-old midfielder Nathan Cartman chanced his arm from long-range.
Cartman went close again after 21 minutes after being played in by Blake but it was the former Bradford player who finally broke the deadlock seven minutes later when he capitalised on more impressive build-up play.
Blake then played an intelligent through ball to provide Beckford with an chance but Shrews keeper Chris Neal got down well to deny the youngster.
Shrewsbury were threatening on the break and got a goal six minutes from the interval when Gavin Cadwallader found himself in acres of space after collecting a long ball over the top and slotted easily past the advancing Jonathan Lund to make it 1-1.
But Cartman restored United's lead after 56 minutes when he shot from distance following more good work by Blake – the strike taking a deflection to leave Neal stranded.
Beckford lifted another effort over the bar and Cresswell also saw a header saved before the former York striker was withdrawn from action 17 minutes from time.
Leeds: Lund, Stansfield, Marques, Hird, Camfield, Cartman (Brown 73), Hutton, Westlake, Blake, Beckford, Cresswell (Ameobi 73).
Unused Subs: Williamson, Edwards, Grace.
Shrewsbury: Neal, Morley (Morris h/t), Leslie, Hall, Jones, Cowan, Humphrey, Adaggio, Cadwallader, Hogg, Williams.
Unused Subs: Barnett, Singh, Draper, Wallis.