A William Gallas header late in the game earned Arsenal three points in a scrappy match with Portsmouth.
The result lifts Arsenal to fourth place in the table above Aston Villa on goals scored.
Gunners boss Arsene Wenger said, "We were lacking a bit of zip because we gave a lot at Aston Villa in our last match.
"It was important that we were intelligent and patient. Portsmouth played very well and they were well organised and defended very deep.
"My team is maturing quite well, and quickly. We will fight for the title and we believe we have a chance."