Left-arm spinner Ojha grabbed four wickets for 20 runs in 12 overs to finish with superb innings figures of six for 47 having grabbed two West Indian second innings wickets last evening. He completed his second five-for in his 14th Test.
Off-spinner Ashwin, who had taken five wickets in the first innings and followed that up with a maiden century to become only the third Indian to perform the all-round feat, claimed four for 14 in 8.2 overs.
West Indies, commencing the day at 81 for two, collapsed in a sensational fashion, losing eight wickets in 23.2 overs for the addition of only 53 runs.
India, who had trailed by 108 runs in the first innings, needed 243 runs in just over two and 64 overs to clinch the Test on a track that offered turn and a bit more bounce.
At lunch, India reached 16 for no loss and need to score 227 runs more in the last two sessions for a clean sweep of the three-match Test series.
Openers Gautam Gambhir and Virender Sehwag were batting without any trouble on nine and six respectively at the break.
When play commenced in the morning, the clutter of so many wickets was little expected on a Wankhede Stadium track on which West Indies batted first to rattle up 590 and India replied with 482.
Ojha, who had sent back Adrian Barath and Kirk Edwards yesterday, bagged four more wickets to complete his second five-wicket haul in an innings in the series as well as his career before Ashwin also got into the wicket-grabbing act.