Ayiah scored a goal in each half — in the 43rd and 52nd minute — to lead the two-time champions into the last-16 stage of the 24-nation event.
After Aiyah’s dominating show, strikers Richard Danso and Emmanuel Toku piled on the agony for the hosts with goals in the 86th and the 87th minute.
Ghana enjoyed 60 percent posession in the game as inexperienced India, playing their first-ever FIFA World Cup in any division, could hardly breach their defence.
It was India’s third straight defeat in the first round. They lost to the United States 3-0 and went down against Colombia 2-1.
In another game, Colombia, who had lost their opener to Ghana, beat the USA 3-1 in Mumbai and booked their last-16 spot by finishing second in their pool.
In Group B action, Mali beat New Zealand 3-1 at Delhi’s Jawaharlal Nehru Stadium to move into the second round.
Meanwhile heavyweights Brazil, Paraguay, France and England have already booked their pre-quarterfinals berth from their respective pools.
Underdogs Iran also made it to the knockout stage earlier this week after thrashing Germany 4-0 to stage the biggest upset of the tournament so far.
The top two teams from each group will book their berth in the last-16 while four other teams, who are ranked third in their pool, could also sneak into the next round.