Monk's men dominated throughout but had to rely on goals from Ki Sung-yueng and Wayne Routledge in the final 12 minutes to finally break Rangers' spirited resistance.
"The message at half-time was to keep on moving the ball quickly and keep our attacking play as sharp as possible," Monk said.
"I felt if we created chances the way we did in the first half then hopefully we would take one or two and secure the game.
"We were able to do that and deserved at least the two goals and the clean sheet.
"People talk about our big wins against Man United and Arsenal, but I look at the details and that was the most complete performance I've seen from us this season.
"For 90 minutes we controlled the whole game - our tempo and passing, our attacking play and defending."
Rob Green was in outstanding form for Rangers with several excellent stops but the former England goalkeeper was finally beaten by South Korean midfielder Ki's first goal at the Liberty Stadium and Routledge added another against his former club four minutes later to secure Swansea's victory.
"I'd mentioned to Ki it was about time he scored a goal so it was funny that he scored," Monk said.
"It was a great finish and it shows everyone is contributing in the team.
"They were two fantastic finishes, it's what we've been working on and it's important as a team to have threats from everywhere.
"I'm very proud of the way we're working and what we're trying to achieve.
"We've put in hours of hard work - tactically, mentally and physically - and we feel we're in a good moment.
"We thrive on it and we're on our biggest points tally we've had since we've been in Premier League and we'll try to push on for the rest of the season."
Rangers' defeat leaves them in the bottom three and still without an away point since their promotion.
But manager Harry Redknapp feels that life on the road has not been helped by the tough sequence of fixtures they've had in the first half of the season.
"We've had hard games," said Redknapp.
"We caught Newcastle on the back of a five-match winning run then we went to Chelsea, Man United and Tottenham earlier in the season when they looked like they were going to be flying
They have not been easy games.
"Look at the table and the teams that have come up - it's a big step up."
Redknapp praised Green's form and said the 34-year-old had responded to the challenge of Alex McCarthy, who joined Rangers from Reading in August.
"Rob Green was in great form
Alex has come in and pushed Rob's game onto another level, he's been fantastic for us," said Redknapp.
"If they score early then you are in for a very long night, but the longer the game goes on at 0-0 then the fans get edgy.
" At 0-0 you are bang in the game and when you get to 12 minutes to go then you are close.
"We've been like that in the last couple of away games at Newcastle and Chelsea and we just couldn't quite hang on there."
Source : PA
Source: PA