A single Owen Farrell penalty separated the teams at half-time but Rob Kearney's converted try just after the break gave Ireland the lead and a Jonathan Sexton penalty extended that to seven points.
But Farrell reduced the gap with a penalty of his own and a try from Danny Care, set up by Harlequins team-mates Brown and Chris Robshaw, handed England victory.
"Obviously every game is huge for us," Brown told BBC One.
"They were unbeaten and we wanted to set a marker today.
"All the boys were outstanding: one to 15, the guys coming off the bench, awesome, we're really happy."
Kearney's try could have easily knocked the hosts on their heels but they responded well and Brown insists they knew they would be fine if they stuck to their gameplan.
"We were pretty happy at half time. Just stick to what we were doing well and just finish off the phases," he said.
"We were just happy to score, we were on the ropes a bit then so that was a massive momentum changer for us.
"I'm just happy we finished it off and got the win."
Head coach Stuart Lancaster claimed the win was the most significant of his two years in charge and was delighted with the way his team dealt with Ireland.
"Given the experience of the Ireland team, the form they were in, the quality of the coaching and the players that they have in their team and some of the relative inexperience we have in our team, I'm just so proud of the boys," he said. "Delighted for them.
"It was a proper Test match, two really good sides going at it.
"I thought Ireland were excellent throughout, scored a try after half-time and really had some momentum with them
"But I thought we showed great maturity in closing out the game and great tries as well so (I am) really, really pleased."
Lancaster was also quick to praise his team's defensive display and, when asked for the key to the win, he said: "I think it was character, spirit, playing for the shirt.
"Ireland, fair play to them, threw everything at us and once we got that lead we just clung on in there."