The British Lions centre was one of five different try-scorers as the Irish followed up their opening RBS 6 Nations win over Scotland with an equally emphatic 37-13 demolition of Italy in Rome.
The inspirational captain, who is the youngest player in the Irish team, touched down in spectacular fashion on 59 minutes for his 18th try, which took him past the previous record held by Brendan Mullin.
"It's a massive honour for me to take over from Brenny Mullin," said O'Driscoll. "He was such a fantastic player when he played for Ireland, Leinster and Blackrock.
"It's lovely to get it but, first and foremost, the important thing was the win."
Coach Eddie O'Sullivan was pleased with an eighth consecutive victory and a second away win in seven days which sets up a likely title eliminator with France in Dublin next month.
"It might not have been as clinical as last week but there was a lot of character in it," he said. "There were periods of the game where we had to work very hard and I think we kept our composure.
"We performed well in the key areas again. Our set-piece was excellent and, by and large, we defended well.
"To score tries from five different backs is a good return for 80 minutes work."
The only disappointment for Ireland, who were without Ronan O'Gara, Givan Dempsey and Shane Horgan through injury, was the loss of prop Reggie Corrigan with a suspected fractured wrist.
"It's to be confirmed but it doesn't look good at the moment," said O'Sullivan. "He was in a lot of pain and we got him off straight away."