Dinda accounted for opener Justin Guillen while Sharma sent back Donovan Pagon as West Indies A went to lunch at 63 for two in 29 overs at the Arnos Vale Sports Complex.
Kraigg Brathwaite was batting on 23 and Nkrumah Bonner was giving him company on 17 at the break after the hosts elected to bat.
Guillen, who was drafted in as a replacement for the injured Leon Johnson, did not last long thanks to Manoj Tiwary who pulled off a sharp one-handed catch at mid-on off the bowling of Dinda.
After accurate first spells by his pacers Dinda and Shami Ahmed, skipper Cheteshwar Pujara introduced Sharma, and the leg-spinner almost immediately made an impact sending back Pagon who lost his leg stump while trying to hit one over the top.
The duo of Brathwaite and Bonner then added 33 runs for the third wicket as the hosts managed to prevent further damage in a session when the bowlers were backed up by some good fielding by the Indians.
Brathwaite and Bonner though did manage to hit a few boundaries off the spinners.
Bonner showed intent when he danced down the wicket to loft Akshay Darekar over his head for a boundary.
Nearing lunch, Darekar seemed to have suffered an injury after a collision with Pujara while chaing the ball, and left the field in pain.
India lead the three-match series 1-0.
