Ramandeep (31st, 34th minutes) scored the field goals just after half-time to give India the upper hand in the Pool B match.
Striker Akashdeep Singh scored another field goal in the 40th minute before Harmanpreet Singh (42nd) powered in a penalty corner to drive home the advantage.
In Pool A, Argentina beat South Korea 2-1.
The experienced Gonzalo Peillat (26th, 53rd) converted two penalty corners while Lee Namyong scored a field goal for the Koreans in the 46th minute.
The first quarter belonged to underdogs Scotland who displayed good attacking skills to put India on the backfoot. They held on to the ball possession for a greater part of the first quarter, keeping the Indians in the hunt.
While Scottish goalkeeper Thomas Alexander was impressive with his saves, it was skipper Grassick who got an early lead for his team with a splendid deflection that beat Indian custodian Vikas Dahiya.
It was a baseline pass by Kenny Bain picked up by Grassick perfectly to stun the Indians.
Both teams slowed down the pace just a little bit in the second quarter. India played cautiously, rotating the ball only to make well-calculated entries into the striking circle.
India's marquee midfielder Sardar Singh was in the centre of action with some impressive dribbling, trying to make space in the circle.
But the Indian forwards were kept from equalising by a determined Alexander who continued to impress with his saves. He padded away Akashdeep Singh's shot on goal in the 25th minute.
The 10-minute break at half-time was put to good use by India's chief coach Roelant Oltmans who brought about strategic changes to create opportunities in the circle.
It worked like wonder with forward Ramandeep Singh finding a breakthrough almost immediately after the restart. He struck a cracker of a goal with a reverse hit from the top of the circle, beating defender Willie Marshall to equalise.
He struck again in the 34th minute when fellow forward S V Sunil produced an assist from the baseline. A perfect deflection by Ramandeep earned India a much-needed 2-1 lead.
In the 40th minute, it was India skipper Manpreet Singh who set up a goal for Akashdeep, who timed his run to perfection to receive the pass and deflect it past Alexander.
In the 42nd minute, a clever-thinking Sunil appealed for video referral that saw India win their first penalty of the match.
India's young dragflick sensation Harmanpreet Singh made no mistake with a brilliant flick, picking up the ball from injector Sardar Singh, to send the ball like a bolt to the top corner of the post.
India did well in the final quarter to defend their lead, denying any opportunity for the Scottish players to score their second goal.
India's young goalkeeper Akash Chikte too held his nerve to ensure India walked away with a 4-1 win.
India will play their next Pool B match on June 17 against Canada.