De Bruyne was at his masterful best as he put City ahead with a lung-bursting run and cool finish.
The Belgium midfielder provided the cross for John Stones to head City's second, then netted again himself before Haaland wrapped up the crucial victory in the final seconds.
City boss Guardiola was delighted to see his two key players shine when the stakes were highest.
"The connection between Kevin and Erling is extraordinary, today we tried to use it as much as possible," Guardiola told BT Sport.
Second placed City are now just two points behind leaders Arsenal with two games in hand.
If City win six of their last seven games they are guaranteed to win the title for a fifth time in six seasons.
Guardiola isn't getting carried just yet however as the Spaniard urged his players to focus on their next three league games.
City travel to Fulham on Sunday, then host West Ham and Leeds.
Guardiola's men are also due to play Real Madrid in the Champions League semi-finals during that period, with an FA Cup final date against Manchester United in June as they chase a remarkable treble.
"I know the next three games are really important. After two games at home against West Ham and Leeds, these three games will dictate if we can do what we want to do," Guardiola said.
"The reality is today we are two points behind Arsenal, they are in front of us."
De Bruyne echoed Guardiola as he refused to say the win had secured another title for City.
"It is too long. We know what people said about whoever won this game but it is so hard, a lot of things can happen," De Bruyne said.
"We have two games in hand but we are still behind them."
On his deadly double act with Haaland, who assisted the Belgian's goals, De Bruyne said: "I think we set up a bit differently. Instead of two number eights I had the freedom to go left or right depending on where the space was.
"We could have scored more. The second half was 50-50 but we didn't give much away.
"They're a class team and hard to play against. We had to be at our best today, and we were."
