The Welsh side were on top for the majority of Tuesday's clash at the Liberty Stadium, but had to wait until the last 12 minutes for the goals that secured all three points.
An inspired display from QPR goalkeeper Robert Green frustrated Swansea until Ki Sung-yueng broke the deadlock with a clinical left-footed finish 12 minutes from time.
Wayne Routledge added a second five minutes later against his former club, who have now lost all seven top-flight away games this season and sit second bottom of the table.
Green had produced fine saves to deny Gylfi Sigurdsson and Wilfried Bony in particular, and the latter also struck a post late on.
Victory for Swansea moved them above Arsenal into sixth place and Monk was pleased with the persistence shown by his side.
"We had to stay patient but I thought it was one of our most complete performances of the season," he told BBC Sport.
"Their keeper had a fantastic game and you do think 'will it be our day?'
"But I said to the players at half-time to stay patient and keep playing the same way and the chances will come.
"They did and we killed it off with two good goals. The performance warranted a clean sheet and those two goals."
