The Welsh side headed into the weekend just three points above the Premier League relegation zone after a dreadful run of form that had seen them win just one of their previous 12 matches in all competitions.
However, Bony eased Swansea's fears with an outstanding performance capped by a clinical brace.
The Ivory Coast international cancelled out Shola Ameobi's opener on the stroke of half-time and kept his nerve to score a 92nd-minute winner from the penalty spot, after substitute Marvin Emnes had been brought down by Cheick Tiote.
Bony, who joined Swansea from Vitesse last July, has now scored 23 goals in all competitions this season and Monk feels the forward's influence has been huge.
The Swansea boss said: "He's been great, Bony. Obviously with (fellow striker) Michu … having an indifferent season with niggly injuries, Bony has stepped up to the plate.
"You can't complain (about) someone that gets 20-plus goals a season in his first season here.
"It's not just that. He's a massive character in our changing room. He works so hard every day, he pushes everyone else.
"If he doesn't score, he is a strength. He's a presence up front and he can be a handful without scoring goals.
"It's even better when he does add goals to it, like you saw here.
"He deserves all the credit. He's been brilliant for us and he can only get better."
