The fourth seed from Thornhill, Ont. lived up to his reputation as one of the rising stars on tour, saving four break points early in the second set and finishing the match with his ninth ace.
The 21-year-old Raonic rose from No. 156 to a career-high 25th in 2011 and was named the ATP Newcomer of the Year. He is currently ranked 31st in the world.
Hanescu is ranked 90th.
Raonic will next meet No. 83 Dudi Sela of Israel, who rallied to beat Benoit Paire of France 4-6, 6-2, 6-4.
Sela went 1-1 against Canada in Davis Cup play in September.
Defending champion Stanislas Wawrinka rallied past lucky loser Edouard Roger-Vasselin 3-6, 6-3, 7-5 .
The Swiss player set up a quarter-final matchup with Japanese qualifier Go Soeda, who beat fifth-seeded Ivan Dodig of Croatia 7-6 (6), 6-3.