An early goal from Mata put Chelsea ahead at Stamford Bridge and was followed by a Frank Lampard penalty, with Arsenal's retaliation from Theo Walcott not enough to counteract the Blues performance.
Following a string of home disappointments, Mata said he was pleased to have contributed to a win at the Bridge.
He said: "It was very important for our supporters after four or five without winning at Stamford Bridge.
"Against our rivals like Arsenal, one of the best in the Premier League, it was a very good win.
"It was important to score in the first minutes and we played more relaxed. In the first half we played really well and created a lot of chances. In the second half... Arsenal have some top players.
"We knew they would try and score and they got a beautiful goal through Theo Walcott. They always play to score and win.
"Today's game was important for us in different ways. We first kept going and reduced the gap to Manchester United and City. Then we played well in front of our supporters, who were very nervous."