I don't think we can start from the middle (higher education), we have to improve our education system at the grass roots level (elementary, middle and high school). Currently our education is completely geared towards mugging something up and vomiting it in the exam. The teachers do not encourage critical thinking. We used to believe that everything written in the textbooks or told is completely the teacher is "gospel" truth and it has been completely proven. No one usually questions or tries to deeply understand what the teacher is saying, but even if someone tries to question something, he is summarily shut down as asking a "stupid" question. So, there is no "research" encouraged at the grass roots level. Same at home. There are certain rules, but parents are unable to explain the reasons behind those rules if their child asks them, so the child has to follow them begrudgingly but does not learn anything in the following of those rules.
Moreover, our society is completely geared towards "making money." There is more to life than making money. Most Indians are living to make money. One should make money to live. Even animals live life without worrying about making money. Why are humans going to the level worse than animals where only thing that matters to them is making money? They don't even know what they will do with that money. It is a RAT race. I think it is an insult to rats to say this because even rats run after food and not after pointless pursuits (unless humans force them in labs). Even a lion does not hunt unless he is hungry or is in danger. Humans are working endlessly to make money. Where is the question of "research" when the only thing you care about is money?
This is happening not only in India but scientific community as a whole. There is very less funding and interest for fundamental scientific research like we had in the first half of 1900s. Now, it is all about solving great problems like "connecting" people through "Facebook." I can assure you that people are only more DISCONNECTED after the advent of facebook. Working for a dating (or worse) website is considered as the EPITOME of one's success in Indian society just because it pays more. Where are we headed?
You ask me for a solution. The solution is education overhaul. Teaching people that money is NOT everything. Human brain is capable of higher thinking and solving complex problems both for humanity and animal/plant kingdom. Difficult questions should be encouraged. We should not be scared of answering difficult questions of our kids. Kids are very inquisitive, but all that is shut down by systematic downplaying of their "stupid" questions. We are teaching kids that making money is the goal of life. What research can such a person do?
I am sorry, but I don't see a more practical solution than this. You can't suddenly create interest to do research in a person at university level. It is possible but is much harder.
At university level, we should encourage students to ask questions which question the fundamental theories. Research begins with encouraging questions. Teachers should be secure enough in their own skins to admit their own limitations. They may not know the answer to the questions, but that should not stop students from asking questions. Nobody in the world may know the answer, but still questions should be encouraged.
I wish there was a point list that I could present to the directors of IITs or MHRD minister that could solve this problem, but there is only so much that they can do. It is a problem of the society and we have to take the initiative to solve it together.