Way made the breakthrough with a deflected shot in the 37th minute and was prominent in midfield throughout.
But it was on-loan Charlton striker Walker - singled out for praise by Town boss Russell Slade - who ran Rovers ragged in attack.
Left up front on his own, the teenage striker worked his socks off and set up Way for his first-half strike.
Until then it had been Doncaster who called the shots, controlling the game with some slick passing football.
Unbeaten in their previous ten league games, Rovers moved the ball about confidently in an entertaining fashion but there was no end product.
Martin Woods had a 20-yard snapshot saved in the 22nd minute and James Hayter had another effort blocked following a corner 11 minutes later.
But otherwise the Doncaster attack was toothless and it was Yeovil who struck first when Way's shot was deflected off the boot of Steve Roberts and looped over stranded keeper Neil Sullivan into the net.
Doncaster were unable to raise their game as they pushed for an equaliser in the second half and Yeovil held firm at the back with Scott Guyett and Terrell Forbes in commanding form.
Town boss Slade won the tactical battle using Gary Dempsey as a holding midfielder to protect the back four, while Paul Warne pressed forward to try and help out in attack.
Yeovil scored again in the 78th minute when veteran striker Marcus Stewart headed home unmarked from around the penalty spot after Anthony Barry had picked him out with a well-flighted free-kick.
Stewart was sent off 11 minutes later for a second bookable offence following a foul on Hayter.
Hayter then headed home from the resulting free-kick only to have the effort disallowed for a push on Steve Mildenhall.
Doncaster did manage to get the ball in the net in a frantic finish when Terry Skiverton turned a shot from Woods into his own net in the third minute of stoppage time.