Karthik, continuing his fine start to IPL-6, delighted the Wankhede crowd with a sizzling 86 off 48 balls.
He was the aggressor during his 132-run stand with Sharma (74 not out off 50) and after his dismissal, the local boy changed gears to take Mumbai to 209 for 5. The 200-mark was crossed for the first time in the competition.
One could not rule out Delhi overcoming the steep target on an ideal batting surface but the visitors could only muster 165 for nine.
David Warner (61 off 37) and Manpreet Juneja (49) tried their best but could not prevent their team from a third straight loss in the tournament. Meanwhile, Mumbai have now won two out of the three games they have played.
The hosts sealed the tie through their supreme batting effort.
Karthik and Sharma took the game away from the opposition after Sachin Tendulkar and Ricky Ponting failed to fire at the top.
Karthik played a blinder and by the time his stay in the middle ended, he had become the leading run-scorer of the mega event.
What stood was out that the wicket-keeper batsman did not play any fancy shot in his innings, his exquisite stroke play was a treat to watch. He ended with 14 fours and a couple of sixes.
Sharma took to the attack after Karthik's dismissal and soon got to his first fifty of IPL-6.
All six bowlers used by Delhi were taken to the cleaners with Ashish Nehra proving to be the most expensive, leaking 49 runs in four overs.
Kieron Pollard (13) did not fire this time and after his departure Sharma was joined by Ambati Rayudu, who hammered 24 off 8 balls towards the end. The last two overs went for 42 runs.
Much like the Mumbai innings, the away team lost a wicket in the first over. Unmukt Chand top-edged one off Harbhajan Singh with Ponting taking a flying catch at extra cover.
What happened next was something that not many would have been imagined a few years ago. Harbhajan ran towards Ponting and hugged the former Australian captain to complete the wild celebration.
Warner and Juneja kept Delhi in the game with their 82-run partnership, but when the Australian got caught in the deep in the 11th over, they were always going to be up against it.