The 11th seed from Thornhill, Ont., who often trains in the Catalan capital during the season, advances to meet sixth-seeded Spaniard Nicolas Almagro on Thursday.
Almagro was a 2011 semifinalist at the real Club de Tenis. But Raonic beat him in a January semifinal en route to the Chennai title.
"I feel my level improved a lot between my first match and this one," said Raonic. "I'm hitting the ball better and feeling well on the court.
"I've not looked ahead to the next match but I will. I like the way my game is feeling on clay and I think I have my chances here. If I can just keep trying to get better and better I'm sure I can do well."
Raonic, currently ranked 25th in the world, dispatched the 82nd-ranked Andreev in challenging, windy conditions that restricted his ace count to a modest five during the 75-minute match.
The Canadian, who trained much of last week after losing to Spaniard Albert Montanes in the first round at Monte Carlo, improved his 2012 ATP record to 18-4. He has two titles to his credit already in 2012.
Raonic's record against Andreev stands at 2-1 after his second clay win against the Russian.
Raonic never faced a break point and broke Andreev three times as he finished the win on his first match point with a dominating second-set performance.
The Canadian also reached the third round in 2011, losing to Croatian Ivan Dodig.