Roma, knocked out of the competition for the last two seasons by Manchester United and with a dismal record in England, had a few chances to pocket an away goal, but Arsenal should have built a bigger lead.
Nicklas Bendtner wasted their best chance shortly after halftime, blazing wastefully over the crossbar. Arsenal will hope Togo international striker Emmanuel Adebayor will be fit to return for what promises to be a tricky second leg.
"It's a regret," Arsenal manager Arsene Wenger told reporters when asked if his side should have killed off Roma. "I'm happy with the performance but there was room to score more goals tonight."
"The one positive, or not the only positive, is that we didn't concede a goal and it puts us into a position where we cannot just defend. We will want to attack and score goals over there."
Without injured Cesc Fabregas in midfield, Samir Nasri took on the responsibility of pulling Arsenal's strings and his speed conjured an early chance for Bendtner.
As halftime approached Arsenal's dominance was rewarded when Bendtner played in van Persie on the left edge of the penalty area and Mexes, who was having a torrid night, got the wrong side of the Dutchman and committed a clumsy foul.
On the restart the home side went for the kill, however, and had chances to extend their lead. Bendtner should have finished off a sweeping move and then Doni saved a low drive from Abou Diaby. Arsenal's profligacy in front of goal continued when Emmanuel Eboue shot wide after over-indulging.
"It was a fair result," Roma manager Luciano Spalletti said. "Their pace and intensity gave us a lot of difficulties but everything will be different in the second match."
