Seb Hines marked his first start of the season with the goal which set Middlesbrough on their way to a second successive league win at the Riverside.
Crystal Palace were behind when Hines, 24, netted his first goal since March, before Merouane Zemmama doubled the lead early in the second half.
Jermaine Easter reduced the deficit from the penalty spot after he had been fouled by Josh McEachran.
But Palace could not force an equaliser as they slipped to a third defeat.
It is the first time Palace have lost their opening three league games for 39 years, but manager Dougie Freedman will not worry too much so early into the season.
However, Freedman will be demanding an improved performance from his defenders after conceding nine times in 270 minutes of action.
Boro broke the deadlock four minutes before half-time when Hines headed home Grant Leadbitter's corner from six yards.
The hosts extended their lead seven minutes into the second half, Zemmama netting from a free-kick after George Friend had been fouled by Wilfried Zaha.
Palace were much improved in the second period and gave themselves a fighting chance when a bad foul by McEachran on Easter resulted in a 55th-minute penalty.
Easter made no mistake from the spot, but Palace were denied a point late on when Boro keeper Jason Steele saved a Zaha effort.
Middlesbrough manager Tony Mowbray:
"It was a bit uncomfortable in the final 15 minutes and we made hard work of it. But any three points is a good three points.
"We gifted them a goal with the penalty and that let them back in it. That changed the psychology of both sides, and they pushed on a bit more and we retreated a bit.
"We were left hanging on, but ultimately it doesn't matter. We got the points and did well with a young team that is only going to get stronger."
Crystal Palace manager Dougie Freedman:
"We haven't played badly today at all. Middlesbrough were good in the first half but we did enough to stay in the game and after the break improved.
"A couple of errors in important areas of the pitch cost us but generally we were OK. We were competitive, we worked hard and we could have got something.
"And it is pleasing that spirit in the squad remains fantastic despite the results so far. If we keep working and believing it will come."
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