""As a test of character it was right up there because of the quality of the Ireland side and I'm chuffed about the whole team's maturity. We had a good first half, but at the start of the second we had a couple of turnovers that put us under pressure," said Lancaster.
"We grew in stature towards the end of the game and deserved our win. We hadn't won here for 10 years and we went and did it. We will take it."
England skipper Chris Robshaw picked up the RBS Man of the Match award for his tigerish display in the back row, while outside half Owen Farrell scored all England's points with four penalties out of five attempts.
Ireland lost outside half Jonathan Sexton with a hamstring injury and wing Simon Zebo with a broken bone in his foot that could keep him out for up to 10 weeks. They had 58% of the possession, enjoyed 57% of the territory, made three line-breaks to England's none and missed only three tackles to England's 11.
The home side also won four line-outs on the opposition's throw, yet couldn't turn their pressure into enough points to build on their opening day win over Wales in Cardiff.
Instead, the cool, calm head on the 21-year-old shoulders of the England outside half Farrell controlled proceedings and steered his side to a third successive win in all internationals - the first time they have achieved that since 2011.
"Credit to Owen who kicked his goals, but from one minute to 80 the squad were top notch. We tightened the game up, ran down the clock and had to be smart - it's a great day," said Robshaw.
"Farrell is brilliant at the moment. He's got a great repertoire of skills, but he's got a great team around him who keep pushing him to get better. We're not going to get carried away."
England now have two home games, against France and Italy, before they head to the Millennium Stadium in Round 5 to face Wales in a game that will be for at least the Triple Crown. Ireland travel to Edinburgh to meet Scotland, four try winners against Italy at the weekend, in their third round match.