Dravid was Royals' top-scorer as they seemed to struggle in the middle before Yagnik, who hit five fours, and Hodge (19 not out) added 57 runs in 27 balls to prop up their side.
They were also helped by some shoddy bowling by Malinga in the last over.
Harbhajan Singh made full use of the overcast conditions returning with figures of 3/23, including the prized scalp of Dravid, before Kieron Pollard took two in one over to further damage Royals' scoring rate after they opted to bat first.
The winners of the match will set up Sunday's summit clash with Chennai Super Kings.
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An interesting duel was on display with a different-looking Dravid taking the attack on Mumbai Indians quickie Johnson, hitting the Aussie for consecutive boundaries with some classical flicks and drives.
That Johnson had troubled Ajinkya Rahane with his rising bouncer hitting the young opener's helmet a while ago, must have surely made the Aussie frustrated.
Finding him at the receiving end, Johnson, who conceded 23 runs from his three-over first spell, was seen losing his cool with some mild exchanges in the middle.
The spinners got some help from the slow track that was aided by the overcast condition.
Ojha, who was introduced in the third over, troubled Dravid, conceding just three runs from his first over.