A third consecutive Premier League game without a win leaves United trailing in City's wake.
City remain top of the league heading into the midweek fixtures, but Liverpool's incredible late victor against Everton in Sunday's Merseyside derby means the gap is still just two points. After the Champions League it is always tough. "People think it's easy for us but that is not the truth, so I like to win in this way", Guardiola said.
It was a landmark moment for former Barcelona and Bayern Munich boss Guardiola, who said: "My 400th win as a manager?"
"We knew we were going to be without the ball for long periods of the game".
Guardiola left City's record goal-scorer Sergio Aguero out of the squad, but even the Argentine star's absence couldn't halt the champions' momentum.
By contrast, the finish for his goal was relatively straightforward, albeit after a stylish build-up, as he fed a pass for Danilo to shoot, then swept in the rebound after goalkeeper Asmir Begovic has failed to hold the ball.
Visiting Bournemouth had shocked their Etihad Stadium hosts with a Callum Wilson equaliser a minute before the break to cancel out Bernardo Silva's 16th-minute opener.
Bournemouth fans will be glad to see the back of him - he now has eight goals in six league appearances against Eddie Howe's side.
Gundogan put the result beyond doubt 11 minutes from time, tapping home from six yards after Sane and David Silva combined to pull the Bournemouth defense apart following a corner.
Palace leapt above Huddersfield in the standings by beating Burnley at Selhurst Park to lift the pressure on manager Roy Hodgson.
Jamie Vardy opened the scoring with a penalty after 12 minutes before James Maddison netted a brilliant volley to move Leicester up to seventh.
Europe is a top priority for the club and Gundogan said the defeats to Jurgen Klopp's side last season showed how they can not afford any slip-ups if they are to win the Champions League. Huddersfield took the lead after 55 seconds, with Mathias Jorgensen heading in from a sliced Bruno clearance.
"We had a lack of rhythm in the first half".
"Football is not for one player the reason why he plays bad".
"We spoke about it at half-time but my speech was ridiculous because it didn't work because the first five or 10 minutes was quite similar to the first half".