MS Dhoni and Ravindra Jadeja have shared an unbeaten sixth-wicket partnership of 127 to guide India to a competitive total of 278-5 in the fourth one-day international against New Zealand in Hamilton.
The pair made 79 and 62 respectively as the tourists, who won the toss, kept their hopes of drawing the five-match series alive.
The first boundary of the day came in the seventh over when Sharma smashed Mills for six.
However, Mills was celebrating moments later, after getting rid of Ajinkya Rahane (3), who became the second victim of the short ball when he picked out Southee at long-leg.
Rayudu was out for 37 four balls later though. His 78-run partnership with Sharma was broken, as he became the third Indian to perish to a short ball. This time Hamish Bennett was the bowler, with Luke Ronchi taking a simple catch.
Assured by the presence of captain Dhoni at the other end, Sharma continued his assault.
However, his knock of 79, which included four sixes and six fours, eventually came to an end in the 33rd over when he tickled a leg-side Kane Williamson delivery through to Ronchi, who juggled with the ball before taking the catch.
Ravichandran Ashwin faced just three balls. He was out for five after cutting Southee to Bennett at third man.
That wicket brought Jadeja to the crease with 101 balls of the innings remaining. The 25-year-old left-hander faced 54 of those deliveries, hitting eight fours and two sixes in the process.
Meanwhile, Dhoni's explosive contribution incorporated six fours and three sixes, including a huge slog over mid-wicket off the final ball of the innings.
Jadeja should have been out earlier in the final over, but bowler James Neesham failed to run him out from extremely close range.