City immediately took control of the game, which was postponed on Tuesday due to heavy rain, and Aguero gave them the lead in the eighth minute when he lifted a cross from Aleksandar Kolarov high into the Moenchengladbach net.
The Argentina striker doubled the home side's lead in the 28th minute when he sent Moenchengladbach goalkeeper Yann Sommer the wrong way from the penalty spot after Christoph Kramer had clumsily brought down Ilkay Gundogan, making his debut in place of David Silva who was rested as a precaution after developing a minor injury in training.
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Aguero completed his hat-trick in the 77th minute from close range after being set clear by Raheem Sterling and Kelechi Iheanacho made it 4-0 in stoppage time.
The goals took Aguero's Champions League tally to 45, overtaking Paul Scholes and Luis Figo, and he has now scored nine times in five games for City this season.
His efforts ensured Guardiola made a successful start to his attempt to join the elite band of managers -- including cross-city rival Jose Mourinho -- who have led two clubs to Europe's most prestigious club honour.
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The Spaniard, who reached the semi-finals in all three seasons with Bayern Munich after winning the competition with Barcelona, praised his team for the efficient manner in which they dealt with tricky opponents. "I know this Borussia team perfectly, I had never won against this coach before. I knew how difficult this would be for us," said the Spaniard. "It was the most dominant performance of my time here, considering the importance of the game. All the players played at a high, high level."
Guardiola saw new signing Gundogan make a highly impressive debut. The German, full of neat control and incisive passing, played for the first time since dislocating the knee that kept him out of Euro 2016.
Three minutes after his clinical early strike, Aguero unselfishly set up Gundogan 10 metres out, but the former Borussia Dortmund midfielder was denied by an athletic save from Sommer.
After two minor alarms -- when Pablo Zabaleta's over-hit back pass evaded Claudio Bravo and a sweet shot by Raffael was deflected by John Stones -- City doubled their lead after Christoph Kramer clumsily brought down Gundogan just inside the box.
Aguero coolly side-footed the penalty home and the only negative of a commanding first-half performance was that the striker required lengthy treatment on his left knee. He hobbled off at half time but reappeared for the second half and, along with Nicolas Otamendi and especially Sterling, threatened Sommer's goal again.
Sterling's fine reverse pass set Aguero clear on goal in the 77th minute and he put the ball through Sommer's legs to complete his hat-trick before Iheanacho converted after superb work by substitute Leroy Sane.
City next face Celtic in Glasgow on Sept. 28 while Moenchengladbach host Barcelona, who dismantled the Scottish side 7-0 on Tuesday.
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