The Premier League club's most expensive ever signing, whose barren run dated back to October 31 last year, ended the drought shortly after the break to set up a fourth-round home encounter with League One outfit Peterborough United.
In freezing conditions at Ashton Gate, the two sides played out a first half in which they were able to muster just one shot on target between them.
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It seemed that the West Brom goalkeeper would be called into action again five minutes later when Wes Burns was sent scampering clear, but the 21-year-old dragged his effort well wide of the target.
Up the other end Craig Gardner fired a half-volley just the wrong side of the post, while the away side's best chance before the break was spurned by Gareth McAuley in the 42nd minute. Again Gardner was involved as he sent a loose ball bouncing back into the Bristol area, only for McAuley to head over the crossbar from close range.
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However, while McAuley had been unable to make the most of his opening, there were no such issues for Rondon seven minutes after the restart. Craig Dawson's cross from the right found the Venezuelan, who chested the ball down before he slotted his shot beyond the reach of rookie keeper Max O'Leary.
It was a relatively muted response from the hosts thereafter as they found it tough to fashion out any opportunities of note.
The most presentable one fell to Aaron Wilbraham just after the hour mark, but the 36-year-old was unable to keep his header down when put under pressure by McAuley.