The home side ended their second innings at 223/6 from 86 overs after resuming their second innings at 26/1, when play was called off in the final session.
The visitors had finished their first innings on day two at 364 all out, after bowling out the hosts for 180 on the opening day.
Ashwin (3/59) impressed with his off-spin as he grabbed two more wickets today after scalping one home side batsman yesterday. Other Indian bowlers struggled to get the wickets.
Shardul Thakur (0/26) and Ravindra Jadeja (1/42) started the day's proceedings, and the Mumbai pacer got some movement immediately. He was on the mark with his line and length, just as in the first innings and troubled the batsmen. However, unlike day one, he was not able to garner any success.
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Jadeja, meanwhile, bowled from the end opposite to the one from where he had sent down 13 overs in the first innings and had finished with 3/16. As such, he struggled with the cross wind across the stadium, and was taken for runs by the two batsmen.
Jadeja did not get any rest though, as skipper Virat Kohli deployed him from the same end as in the first innings. And it paid immediate dividends as Jadeja got his man, with Campbell caught at mid-on by Lokesh Rahul.
At the other end, Ashwin continued to trouble the batsmen with his bounce and turn while bowling to an attacking field. But Shai Hope (17) and Jermaine Blackwood (51) defied him for nearly five overs.
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Mohammed Shami (1/22) returned thereafter to bowl a four-over spell, while Amit Mishra (0/17) was deployed as well. But Blackwood, in company of Vishaul Singh (39), managed to bat on for nearly 17 overs and put on 34 runs for the fourth wicket going into the lunch break.
Soon after that, the match lost all steam as Stuart Binny (0/11) and Murali Vijay (0/34) were brought on to bowl.
The drab proceedings had little by way of cheer, except the odd wickets that fell. Singh was run-out, as Shikhar Dhawan's throw from the deep beat him to the striker's end. Rahul was keeping wickets then and had no hesitation in removing the bails.
Rahkem Cornwall (21) then continued his hard-hitting ways from the first innings and smacked one four and two sixes as Shami got another spell. The Bengal pacer had been toiling without reward since day one, and finally got a wicket to show for, as Cornwall edged down leg-side to Wriddhiman Saha, who returned for keeping duties in the final session.
The game meandered for a while as West Indies Board President's XI finally got past the Indian lead and went ahead for once, thanks in part to Vijay and Cheteshwar Pujara (0/10) bowling a spell in tandem. Montcin Hodge was unbeaten on 39.
WICB President's XI: 180 all out and 223 for 6 in 86 overs (Vishaul Singh 39, Montcin Hodge 39 not out; R Ashwin 3/59).
India: 364 all out in 105.4 overs.