The game's first half-chance fell to Glenn Murray, who looped a header over the bar after meeting a good ball into the box.
It was a quiet start to the contest, and Charlton would have been happy with the way they quietened the home fans.
Jordan Obita tried to find a way past the Addicks' resolute defence but his low drive was blocked in an exchange that typified the early stages of the match.
Vetokele eventually got the goal that the visitors deserved when he headed home from Chris Solly's delivery.
Reading should have equalised just before the break, with Simon Cox's initial shot deflecting wide just before Murray's header flew past the wrong side of the post from a corner.
Murray continued his efforts to get the Royals back in the game after the restart as he turned and fired at goal from 25 yards out but his effort was comfortably saved by Stephen Henderson.
The keeper could do nothing about Oliver Norwood's drive, however, which flew past him and struck the post in what was a let-off for the away side.
Despite forcing Charlton back into their own half for long spells the Royals could not find an equaliser, meaning that the visitors left with all three points.