Paceman Zaheer took two wickets in successive balls before spinner Ravichandran Ashwin made it three for the addition of nine runs as Australia's middle order folded to leave the hosts reeling on 214-6 at a packed Melbourne Cricket Ground.
But Haddin (21) and Siddle (34) rode their luck and survived a raft of appeals to add an unbeaten 63 for the seventh wicket, guiding the hosts to 277-6 at the end of the first day of the four-test series.
Zaheer's fiery afternoon spell ignited the Indian attack after debutant Ed Cowan and captain Michael Clarke had threatened to get on top of the tourists.
Mike Hussey's dismissal, caught behind for a golden duck off Zaheer, left the number six furious and television replays appeared to show the ball missing his glove on the way through to India skipper MS Dhoni.
But with the tourists having thumbed down the use of the replay technology before the series, Hussey had no recourse to appeal against umpire Marais Erasmus's decision and trudged off cursing.
Erasmus later turned down a raft of appeals, one off Zaheer's bowling that appeared to trap Haddin plum in front in the final overs.
Amid the drama, Haddin and Siddle stood firm to frustrate the bowlers as shadows crept across the ground.
Resuming on 170-3 after the tea interval, Clarke and Cowan added a brisk 45 for the fourth wicket before Dhoni threw the ball back to Zaheer, who had struggled for rhythm in his first test after a four-month injury layoff.
The 33-year-old found his line in devastating fashion in the 12th over after tea, beating Clarke with a sizzling rising delivery that faded away wide from off-stump, then having him chop onto his stumps for 31 with the next ball that cut back in.
Zaheer then fired a scintillating bouncer that had Hussey leaping at his crease before the ball thudded into Dhoni's gloves as Indian fans roared.
After a big appeal, umpire Erasmus raised his finger amid the din, leaving Hussey shaking his head in disbelief.
Haddin flicked a single off his pads to deny Zaheer a hat-trick and briefly quell the tumult, but spinner Ashwin kept the momentum rolling by dismissing Cowan for 68 three overs later.
Ashwin coaxed Cowan into playing a poorly timed cut-shot that served only to nick a feathered catch to Dhoni.
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