Chasing a huge 189, Kolkata reached the target in the last ball with McCullum (48-ball 81) and Hodge (71 not out from 44 balls) setting the SuperSport Park on fire to give Kolkata their second victory from 13 matches and in the process denting Chennai's chances of making it to the semifinals.
Kolkata's win does not make any difference to their chances as they are already out of semifinal contention though it must have given them the satisfaction of beating a strong side.
For Chennai, still second on IPL table with 15 points from 13 matches, they will have to win their last match against Kings XI Punjab on May 20 in Durban and wait for other results to see if they make it to the last four stage.
McCullum gave Kolkata to a flying start with an exhibition of stunning batting racing to his second IPL-II fifty in 21 balls though he did not get enough support from the other opener, Sourav Ganguly.
Hodge, who shared a 90-run stand for the second wicket with McCullum from just 56 balls, joined the party towards the close of run chase with some stunning fours and sixes to take his side home in the last ball.
Out-of-sort Ganguly's (4 from 14 balls) dismissal in the sixth over did not distract McCullum and he sent the Chennai bowlers for a leather hunt with superb display of batting before he was out in the 14th over off Shadab Jakati. His
superb knock included 11 fours and three sixes.
Kolkata needed 58 from the last five overs with eight wickets in hand and after David Hussey (3) was run out while going for a non-existent single the asking rate rose to above 13 per over.
Hodge, who hit four fours and equal number of sixes, kept Kolkata in the hunt with some stunning shots, including two sixes off Laxmipathi Balaji in the penultimate over.
Wriddhiman Saha also played his part with an unbeaten 13-ball 25 and sharing a 56-run stand from just 28 balls for the unbroken fourth wicket, besides hitting the winning runs off Suresh Raina from the last ball of the innings.
Earlier, playing without IPL-II top scorer Matthew Hayden, Chennai opted to bat first and scored an imposing 188 for three, mainly revolving around Suresh Raina's (52) superb half century and captain Mahendra Singh Dhoni's unbeaten 40.
Raina cracked his fifth IPL fifty with a 37-ball 52 which included three fours and three sixes while Dhoni carried his bat through the innings with a 28-ball 40 which was studded by four fours and a six.
Dhoni, who was dropped by Murali Kartik while on 16, shared a 74-run stand with Raina for third wicket from just 47 balls and then an unbroken 36-run fourth wicket partnership with Albie Morkel from just three overs.
Chennai were off to a quick start with Parthiv Patel and George Bailey bringing up 50 in the sixth over. Australian Bailey did not shy from taking risks by hitting over close-in fielders for boundaries, capitalising on field restrictions of
But, two run outs of the two openers from direct throws by same fielder, Laxmi Ratan shukla, suddenly slowed down the momentum.
Parthiv Patel fell for a 19-ball 25 in seventh over while Bailey could score 29 from 26 balls (4X4) and from 59 for no loss, Chennai slumped to 82 for two by the strategy break.
Chennai found scoring a tad difficult when the spinners Ajantha Mendis, Murali Kartik and Brad Hodge were operating, but with wickets in hand, they stepped on the gas after the halfway mark.
A big over, which fetched 13 runs, off David Hussey was followed by a superb 15th over bowled by Ashok Dinda who gave away just two runs.
But, Raina hit Ajantha Mendis for two sixes to take 17 runs from the 16th over. Raina then brought up his fifth IPL fifty in style hitting Ashok Dinda for a six before he fell next ball caught by Shukla for a ball 52.
Chennai took 19 from the last over bowled by Ajit Agarkar with Albie Morkel hitting two sixes and a four.