Arsene Wenger's side dominated the match but, with such a slim lead to take into the second leg in a fortnight, there is still everything to play for.
Arsenal made two changes from the 0-0 draw against Sunderland at the weekend. Emmanuel Eboue started instead of Alexandre Song, and Abou Diaby replaced the cup-tied Andrey Arshavin, who had already played for Zenit St Petersburg earlier in the competition.
Arsenal came into the game on a 13-unbeaten run dating back to their last Champions League match away to Porto in December. However, their last three home matches had all been 0-0 draws. Roma have lost their five previous matches on English soil, all in the last four seasons.
Arsenal took control of the game from the start, causing Roma plenty of problems. Samir Nasri was a constant threat and Gael Clichy caused Roma's full-backs all sorts of problems, as he was able to get down the wing and whip balls into the box.
It wasn't until the 17th minute that Roma had their first attack of the game when Manuel Almunia had to pull off a fantastic save and push the ball away for a corner.
Diaby, who has missed the last three games with a thigh strain, had plenty of the ball early on as Roma's midfield failed to gain possession and when they did get the ball, panic set in as they gave it away needlessly.
In the 37th minute van Persie put Arsenal 1-0 up after calmly slotting a penalty into the bottom right-hand corner. Van Persie had won the penalty himself after being brought down in the penalty area when he received a pass from Nicklas Bendtner.
In the 53rd minute Bendtner missed a glorious chance after receiving the ball in the penalty area ut, with just the keeper to beat, he failed to hit the target.
In the 66th minute Simone Loria, who had a torrid time in defence, failed to clear the ball and Eboue was through on goal with just Doni in the Roma goal to beat, but he wasted the opportunity to put Arsenal 2-0 up after failing to hit the target.
With 14 attempts on goal, but only two on target, Arsenal will be wary of only taking a one-goal lead into the second leg in a fortnight.