Juninho scored his first goal for Celtic to kill off Hearts in Glasgow.
Henri Camara and Juninho both scored for Celtic
Hearts adopted the defensive system likely to be used in the Uefa Cup in midweek and a David Marshall save from Paul Hartley denied them the lead.
But Henri Camara eased Celtic's nerves before half-time by giving them the lead with a stunning volley.
Juninho then side-footed home, Hearts' Steven Pressley missed his first-ever competitive penalty before John Hartson headed in Celtic's third goal.
Celtic manager Martin O'Neill had welcomed back influential Jackie McNamara, who damaging his ankle against Barcelona a month ago.
He took the place of Bobo Balde in defence, while Ross Wallace came in for the injured Joos Valgaeren.
Graham Weir came in for Dennis Wyness up front for Hearts.
Hearts and Scotland goalkeeper Craig Gordon was busy early on and he had to punch away Camara's back header in the fifth minute from Stilian Petrov's corner.
The on-loan Wolverhampton Wanderers striker had the ball in the back of the net when he stooped to head Petrov's cross into the bottom corner, but the linesman flagged for offside.
The visitors appealed in vain for a penalty when Weir went down in the box under the challenge of Chris Sutton.
Celtic goalkeeper Marshall prevented Hartley giving Hearts a 24th-minute lead when he pushed the midfielder's low drive past the upright.
Gordon saved at the other end from Hartson before Camara broke the deadlock, volleying Hartson's knock-down into the top corner of the net from eight yards.
Hearts head coach Craig Levein made a change before leaving to watch Uefa Cup opponents Feyenoord, Kevin McKenna came on for Weir at half-time to become Hearts' lone striker.
Levein missed his side going two behind after 57 minutes, when Juninho exchanged passes with Hartson before side-footing the ball past Gordon.
Hearts were handed a chance to bounce back into the game after 69 minutes, when McNamara was ruled to have handled in the box.
But Pressley's spot kick struck the post.
Gordon prevented Celtic going three ahead with a superb save from a Hartson drive.
The Hearts goalkeeper blocked another effort clear with his feet, but Wallace turned the ball into the path of Hartson to take advantage and score.
Celtic: Marshall, Agathe, Varga, Sutton, McNamara, Lennon, Petrov (McGeady 85), Wallace, Juninho Paulista (Sylla 82), Camara, Hartson (Lambert 82).
Subs Not Used: Hedman, Pearson, McManus, Cuthbert.
Goals: Camara 41, Juninho Paulista 57, Hartson 82.
Hearts: Gordon, Maybury, Pressley, Webster, Neilson, Kisnorbo, Stamp (Hamill 85), Hartley, Stewart (Wyness 67), McAllister, Weir (McKenna 45).
Subs Not Used: Moilanen, MacFarlane, Berra, Elliot.
Booked: Pressley, Maybury, Neilson.
Ref: K Clark