Published: 2017-03-11 23:06:12 BdST
David Silva gave them a third-minute lead and Sergio Aguero struck again in the 67th minute, with the visitors missing numerous chances to win by a bigger margin.
"We are so happy to be there," Guardiola told reporters after a solid display ahead of Wednesday's Champions League last-16 return leg at Monaco, where City will defend a 5-3 lead.
"We made a good performance, we were there from the beginning. The game should be over 30 minutes before but we missed a few chances."
Guardiola's attacking formation, featuring Silva, Raheem Sterling, Kevin De Bruyne and Leroy Sane behind Aguero, paid instant dividends as City carved open the home team's defence.
Yaya Toure fed Pablo Zabaleta on the right flank with a defence-splitting pass and the Argentine defender drove a perfect ball across the face of goal for Silva to shoot home from close range.
Middlesbrough kept getting undone on either wing as the lively Sane and Silva gave their markers a roasting and the home team's goalkeeper Brad Guzan made a string of good saves.
Aguero hit the woodwork after another lightning raid down the right but made no mistake when he steered a first-time shot past the helpless Guzan at the near post from a fizzing low cross by Sane.
City threatened to run riot in the closing stages as acres of space opened up, but Guzan spared the home side a heavier defeat by denying Sterling and Silva.
"When you attack good, you defend good," said Guardiola, still in the hunt for three trophies in his first season at City.
"We defend 40 metres away. I always believe that when the ball is far away from our goal we are safe," the Spaniard added.
"I’m confident ahead of Monaco, but not for the result. I’m confident because I am pleased the most as I like to work with these guys, I’m so happy."
Arsenal host non-league Lincoln City in the second FA Cup quarter-final later on Saturday.