The in-form striker netted the winner midway through the second-half to ensure Tony Mowbray's side, who had Joe Bennett sent off, maintained their unbeaten start to the season.
After a fine start to the campaign, Palace failed to get on the scoresheet for the first time this season as Jermaine Easter was denied by the crossbar late on.
The Eagles slipped to their second consecutive Championship defeat and their first home loss of the campaign.
The hosts had the opening chances of the match.
Defender Patrick McCarthy, who scored against Leeds last week, headed Darren Ambrose's corner over before Easter, after a surging run, struck a fierce shot from 25 yards that Boro goalkeeper Carl Ikeme had to tip over the crossbar.
Palace continued to attack and Ikeme was tested again, this time Jonathan Parr was denied from 20 yards.
Finally, after plenty of early possession, Boro had their first chances. Barry Robson had a shot blocked before Eagles shot-stopper Julian Speroni was tested for the first time after 25 minutes from an ambitious Joe Bennett 30-yard effort.
Robson had another effort from distance but Speroni gathered with ease.
After hesitant defending from Boro's back-line, the ball fell to Parr but the midfielder drilled his 25-yard strike over the crossbar.
Striker Sean Scannell was a thorn in Middlesbrough's defence, attacking at pace, and was unlucky not to provide the opener when Ikeme almost parried his deflected shot into the path of fellow frontman Easter.
With the final act of the first half, Faris Haroun headed Robson's teasing corner over the crossbar.
Mile Jedinak, five minutes after half time, tested Ikeme but the goalkeeper was equal to the midfielder's 20-yard strike, before Easter's snap shot flew over the crossbar.
Speroni had to tip over a Justin Hoyte cross and, after Palace failed to clear from the resulting corner, the visitors broke the deadlock against the run of play after 65 minutes when Emnes found the net from a tight angle.
Substitute Wilfried Zaha, replacing Ambrose, almost made an immediate impact but failed to find an end product after a mazy run through the Boro defence.
The game sparked into life after 75 minutes when Boro were reduced to 10 men after Bennett was given a second yellow card for bringing down the lively Zaha.
Zaha, after a lucky break, squared the ball to Easter but the striker fired against the bar eight minutes from time.
Despite four minutes of added time, Murray could only head straight at Ikeme, while Emnes should have wrapped up the game with the last kick of the game but he fired wide.