Geoffrey Kondogbia???s deflected effort put the visitors in front, before former Tottenham striker Berbatov smashed Monaco further ahead in the second half as Arsenal failed to put away their chances
Olivier Giroud and Danny Welbeck missed glorious opportunities to bring the hosts back in it before Alex Oxlade-Chamberlain pulled one back in stoppage time, but Yannick Ferreira-Carrasco restored Monaco’s two-goal cushion.
It???s the first victory for a French side at the Emirates Stadium and leaves Arsene Wenger’s side on the brink of an exit at the last-16 stage for the fifth season in a row.
Arsenal enjoyed plenty of possession in the early stages, but were in no rush to force the tempo as Monaco started the game putting little pressure on the hosts.
Danny Welbeck was almost in early on as he latched on to Francis Coquelin???s ball over the top, spinning past Elderson, but he couldn???t direct a shot anywhere near the target.
It was to be one of the Gunners??? better passages of play in the half as they regularly saw attacks break down with loose passing in and around the box.
It took until the 33rd minute for Wenger???s men to fashion another good chance as Sanchez burst through the middle and found Ozil, who returned it to his team-mate inside the area. The pass was slightly behind the Chilean, though, and he had to work the ball out of his feet before dinking a shot over the crossbar.
Five minutes later Monaco???s opener came as Welbeck was dispossessed on the halfway line and the visitors advanced into the Arsenal half. Almamy Toure and Joao Moutinho worked the ball into Kondogbia, who fired a 30-yard effort at goal which took a deflection off Per Mertesacker and flew past David Ospina into the middle of the goal.
Arsenal came out with intent in the second half, Cazorla causing problems for the Monaco defence. The Spaniard won a free kick which he then whipped into the area, but Giroud could only head over the bar from close range.
He was immediately made to pay for the miss as the visitors raced up the other end and, with Per Mertesacker caught well out of position, Anthony Martial was played in behind before he squared for Berbatov, who smashed a low shot past Ospina to double Monaco???s lead.
Giroud spurned the best chance of the night just a few minutes later, as Alexis Sanchez darted into the box and rifled a low shot which Danijel Subasic parried straight to the Frenchman, who blasted the rebound over with the goal at his mercy.
Welbeck then had a similar opportunity as substitute Theo Walcott saw an effort saved, only to get in the way of his team-mate???s effort on the rebound which flew over the crossbar.
Oxlade-Chamberlain came on late and looked to have given the hosts hope as he picked the ball up on the edge of the box before curling a superb 20-yard strike into the top corner in the 91st minute.
But Monaco had time to restore their two-goal cushion as Oxlade-Chamberlain was caught in possession, and substitute Carrasco was played in behind before drilling a low shot across Ospina and in off the far post to seal a superb victory for the Ligue 1 side.