Powar, Raina and Vikram have all played One-dayers for India but have yet to turn out in a Test.
"We decided to select the team keeping an eye on the future," said chief selector Kiran More. "We had discussions with the team management in the West Indies before announcing the squad."
Powar, who has played 12 One-dayers, was picked ahead of young leg-spinner Piyush Chawla to back off-spinner Harbhajan Singh and veteran Anil Kumble.
Left-handed Raina, 19, was rewarded with a berth after impressing in his 23 One-day appearances while 21-year-old Vikram was preferred to Ajit Agarkar, who is playing in the ongoing One-dayers in the Caribbean.
"Vikram has done well in domestic cricket and we have been fairly impressed with him. In the past too we selected young players like Sreesanth and they have proved themselves," said More.
"Also, Agarkar has been a fine One-day player but his performances in Tests have not been that impressive," he added.
Apart from Agarkar, left-arm seamer Rudra Pratap Singh and batsmen Robin Uthappa and Venugopal Rao will return home after the One-dayers.
Kumble and experienced batsman Venkatsai Laxman will leave for the West Indies along with Vikram, opener Wasim Jaffer and wicket-keeper Dinesh Karthick, a stand-by for Mahendra Dhoni.
"We are sending a second wicket-keeper in Karthick but could not fit in a third opener in the squad," said former India wicketkeeper More.
The selectors chose Kumble and Laxman as expected but continued to ignore former skipper Sourav Ganguly, despite the absence of star batsman Sachin Tendulkar because of a shoulder injury.
Kumble has bagged 510 wickets in 106 Tests while Laxman has 4,441 runs in 73 Tests with nine centuries.
India are scheduled to play the opening Test in Antigua from June 2 to be followed by matches in St. Lucia, St Kitts and Jamaica.
The squad: Rahul Dravid (capt), Virender Sehwag, Wasim Jaffer, Venkatsai Laxman, Mohammad Kaif, Yuvraj Singh, Suresh Raina, Mahendra Dhoni, Dinesh Karthick, Ramesh Powar, Harbhajan Singh, Anil Kumble, Irfan Pathan, Shanthakumaran Sreesanth, Vikram Rajvir Singh, Munaf Patel.