Resuming their innings at 60-1, India produced a solid batting performance as Rahul and Parthiv complemented each other and completed their well-deserved half-centuries to lay the foundation for a good total.
While Rahul took 96 balls to score his fifty, Parthiv achieved the feat in 84 deliveries as the duo shared a 152-run partnership for the opening wicket at the MA Chidambaram Stadium.
It was spinner Moeen Ali, who finally broke the stand when he had Parthiv caught by Jos Butler at cover after the wicket-keeper batsman tried to repeat a shot which had earned him a boundary earlier in the over.
Pujara then joined Rahul and the duo scored 21 runs off 37 balls.
Earlier, Rahul made his intent clear in the morning when he blasted spinner Liam Dawson for a couple of sixes at the long-off and long-on boundary.
The 24-year-old from Bangalore soon notched up his first half-century of the series by taking a couple in the 28th over off Stuart Broad. He then picked up a boundary off the pacer between the mid-on and midwicket area.
Parthiv also had sent one past the short midwicket area in the first ball off Broad for a four as the duo brought up the team hundred in 175 balls in the 30th over.
The openers continued to deal in boundaries with Rahul smashing Jake Ball through point and then sweeping Ali through square leg and Parthiv managing to tickle one past the wicketkeeper in Jake's over.
After a few silent overs, Parthiv hit Adil Rashid through the cover for another four in the 37th over, while Rahul reverse swept Ali for another boundary in the next over.
In the 42nd over, the India wicketkeeper batsman lifted Ali over midwicket for a boundary before falling to a similar shot in the fifth ball.
Newman Pujara then warmed up with a couple of fours off Rashid in the 47th over.
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