Symonds, bowling his off-spinners, trapped stoic Dravid leg before wicket for 16 three balls before lunch on the fourth day.
Faced with an improbable target of 499 runs for victory over two days, the Indians went to lunch at 56 for two with V.V.S. Laxman unbeaten on 21 and Sachin Tendulkar, playing in his farewell MCG Test, on two.
Dravid, who scored five off 66 balls in the first innings, again stonewalled the Australian bowlers facing 114 balls in 150 minutes with two boundaries.
But Symonds finally got one through his defences hitting his back pad on the low, slow drop-in MCG pitch.
Laxman was slightly more animated than Dravid and had occupied the crease for 55 balls with three fours.
The Indians faced 27 overs of attritional cricket in the morning session with 13 of them maidens and scored 50 runs.
India require a supreme effort of concentration and patience from their experienced middle order to draw the Test or bring off a miracle victory against the world No.1 side.
Only three teams in Test cricket history have scored 400 or more in the fourth innings for victory.
Adam Gilchrist overtook Ian Healy as the Australian wicketkeeper with the most dismissals with his catch of opener Wasim Jaffer for 15 off Brett Lee.
The regulation catch was Gilchrist's 396th dismissal in his 93rd Test passing his predecessor Healy's 395 from 119 Tests.
South Africa's Mark Boucher, currently playing in the first Test against the West Indies in Port Elizabeth, holds the wicketkeeping record with 406 dismissals.
Jaffer had been caught by Gilchrist off a no-ball off the first delivery of Lee's seventh over, but was on his way two balls later to the same mode of dismissal 33 minutes into the fourth day's play.
It was an unproductive match for Jaffer, who had averaged over 51 this calendar year with three centuries.
Lee claimed his fifth wicket of the Boxing Day Test and his 252nd Test wicket, the sixth all-time leading Australian wicket-taker.