Guidetti and Scepovic scored the goals at Celtic Park after the visitors had Manuel Pascali dismissed on 34 minutes.
Referee Willie Collum had no option other than produce a red card to Pascali after the Killie defender hauled back Scepovic as he burst through towards the penalty area.
Kilmarnock’s misery was compounded within 60 seconds when Guidetti curled the resulting free-kick from 20 yards beyond Conor Brennan.
Celtic sealed the victory on 64 minutes when Emilio Izaguirre and Wakaso Mubarak combined on the left to set up Scepovic at the far post where the striker steered the ball home.
Killie started brightly and Craig Gordon had to race from his line to thwart Temitope Obadeyi before Stefan Johansen got across to ensure Josh Magennis was unable to score from the rebound.
Callum McGregor was lively and he beat to set up Scott Brown, whose shot was blocked, and the winger later delivered the ball to Wakaso at the far post but his header was straight at Brennan.
And McGregor was denied by a last-gasp challenge six minutes before the break before Mark Connolly headed the rebound from Scepovic off the line.
A minute later a swerving shot from Guidetti deflected inches wide, and there was still time for Wakaso to shoot narrowly beyond the far post from distance before the break.
In the opening minute of the second half McGregor played in Scepovic and his rising effort was parried by Brennan.
Guidetti hammered a shot against the post on 59 minutes and the Celtic striker was denied moments later by a brilliant save from Brennan.
Brennan got across to his right to make a save from Wakaso after Izaguirre created the chance with a cross.