Boro had excellent chances to open the scoring in the first period, with Admana Traore and Gaston Ramirez both coming close in the opening half.
They continued to dominate in the second period, with chances from Alexis Sanchez, Traore, and Mesut Ozil, but nobody could find a net.
Nobody will have expected Aitor Karanka's to do much as they took on Arsene Wenger's side, who are in a good vein of form, but Boro came flying out the traps from the off.
Their first chance came 20 minutes in, when Laurent Koscielny failed to clear Alvaro Negredo's flick, the ball was stolen by Traore who went through on goal and Petr Cech did brilliantly to deny the Spaniard.
They came even closer a moment later, with Ramirez curling a free kick which looked destined to rustle the back of the net, but his effort came back off the corner of the post and the crossbar.
Arsenal had their first look at goal in the 23rd minute, with Sanchez trying his own hand at curling home a free kick, but Victor Valdes was there to batter the ball away from danger.
Cech was on hand once again to produce yet another excellent save. A cross in was flicked on by Negredo, which found Ramirez at the back post, but Cech was there to get behind it to preserve the score.
Keeping up the pressure
Karanka's side showed no let up as they came out for the second period, however, the Gunners began to show some danger in the match.
Sanchez had the first real opportunity of the second period, with the Chilean trying one from 20 yards, but Valdes did well to tip his effort away.
Traore had proven a danger throughout the match, and produced a piece of excellence just before the hour mark. He went on a mazy run having picked up the ball in his own half and got beyond Francis Coquelin, but Cech was there again to deny him.
Arsenal's best opportunity of the game came in the 68th minute. Sanchez was put through on goal by Theo Walcott, but the angle didn't work for Sanchez as it proved easy for Valdes.
Right at the death
Both sides were still going for what would have been the winning goal, and both sides had great chances to seal the three points.
Negredo looked to be the hero as he was clean through on goal in the 89th minute, but a excellent last-ditch tackle from Koscielny gave the Gunners a chance.
The Emirates was in a frenzy in stoppage time as Arsenal had the ball in the net, a shot-cross from Alex Oxlade-Chamberlain found it's way to Ozil who stuck it home, but the flag was up for offside.