Jermaine Beckford scored twice as Leeds made it six wins out of six and moved off the bottom of League One.
Beckford put the visitors ahead with a flicked volley from Seb Carole's ninth-minute cross.
Rovers trio Craig Disley, Andy Williams and Lewis Haldane were off target with headers before Tresor Kandol converted David Prutton's cross on 77 minutes.
Beckford's overhead kick made it 3-0 as Leeds scored their first points after wiping out a 15-point penalty.
Bristol Rovers: Phillips, Ryan Green (Jacobson 79), Anthony, Elliott, Carruthers, Igoe (Pipe 76), Campbell, Disley, Haldane, Lambert, Williams (Walker 69).
Subs Not Used: Hinton, Rigg.
Leeds: Ankergren, Richardson (Huntington 90), Heath, Marques, Hughes, Prutton, Douglas, Clapham, Carole (Westlake 78), Beckford, Kandol.
Subs Not Used: Lucas, Howson, Flo.
Booked: Douglas, Carole.
Goals: Beckford 9, Kandol 77, Beckford 90.
Ref: Keith Stroud (Hampshire).