Balde added a third just before the end to put a better gloss on the result, but the loudest cheer of the night was when Hearts equalised in their game against Rangers.
However even that enthusiasm was dispersed by the final result at Tynecastle which still leaves Celtic six points behind Rangers albeit with two games in hand.
In a flat atmosphere Celtic fans had little to cheer about in the first half. Petrov struck a shot straight at Derek Soutar in the Dundee goal before the Bulgarian midfielder pulled another effort wide from Alan Thompson's pass.
Dundee threatened twice in as many minute when Fabian Caballero's pass found Neil Barrett in an advanced position, but he blazed his shot wildly over.
There was an even better chance for Steve Lovell shortly after, but he shot weakly into the grateful arms of Rab Douglas from six yards.
A patient build-up by Celtic ended with Jackie McNamara shooting narrowly over. Then from a McNamara cross, Chris Sutton timed his run perfectly but his powerful header was straight at Soutar.
Stanislav Varga was also guilty of placing his header from Petrov's cross too close to Soutar and after some skilful footwork, Sutton's left-foot effort flew wide.
The home crowd's jeers at half-time turned to cheers when Petrov scored with a powerful header from McNamara's cross when he was left unmarked at the back post just after the restart.
Soutar performed heroically to deflect John Hartson's piledriver on to his bar and over before Balde scored Celtic's second.
The giant centre-back was left unmarked in the six-yard area to head home easily Petrov's corner.
Thompson's 25-yard swerving shot was well saved by the Dundee keeper as Celtic threatened to run riot, but it was only the few fans who remained until the bitter end who were rewarded with a third goal when Balde again headed home a Petrov cross.