Aguero struck his second treble of the season as substitute Kelechi Iheanacho completed the scoring in stoppage time in front of just 32,000 fans – a figure hit by Tuesday’s postponement due to heavy rain.
City followed the lead of Guardiola’s old club Barcelona, who thrashed Celtic 7-0 at Camp Nou, by laying down a marker in their group-stage opener.
“Aguero is one of the best because of his special quality in the box. He is a special, special player,” said Guardiola. “There have been seven official games and we have won all of them. Every time we play better and better.”
Aguero converted from close range following Aleksandar Kolarov’s driven eighth-minute cross, and doubled his tally shortly before the half-hour mark from the penalty spot. The 28-year-old skipped around Monchengladbach goalkeeper Yann Sommer to complete his hat-trick inside the final quarter of an hour before Iheanacho rifled home a late fourth.