With Charlton drawing 1-1 at Yeovil, the Whites took full advantage and ruined former assistant manager Gus Poyet's unbeaten start as Seagulls boss.
Snodgrass fired in the opener from 20 yards on 27 minutes and top scorer Beckford bagged his 13th of the campaign from Kilkenny's pass two minutes before the break.
Provider then turned scorer with the third goal in the final minute after a brilliant run by substitute David Prutton.
Brighton & Hove Albion (4-4-2): G Smith — A Whing (sub: A Navarro, 69min), T Elphick, J Tunnicliffe, A El-Abd (sub: C Davies, 78) — E Bennett, A Crofts, G Dicker, D Cox (sub: K McLeod, 69) — G Murray, N Forster. Substitutes not used: J Pelling, D Livermore, G Hart, A Virgo.
Leeds United (4-4-2): C Ankergren — L Bromby, P Kisnorbo, L Michalik, A Hughes — J Howson (sub: D Prutton, 81), N Kilkenny, M Doyle, R Snodgrass — S Vokes (sub: E Showunmi, 83), J Beckford (sub: M Gradel, 90). Substitutes not used: A Martin, M Grella, A Robinson, A White. Booked: Michalik.
Referee: J Linington. Attendance: 7,615.