Laporte's celebrations of a long-awaited France call-up this week appear likely to be short-lived after he was taken off on a stretcher in the first half.
The 25-year-old went down in discomfort after a collision with Adam Webster, an incident that is sure to give Pep Guardiola several sleepless nights over the international break.
City was leading courtesy of Kevin De Bruyne's second-minute opener and Aguero added two more either side of the interval before teeing up Bernardo Silva to add the icing 17 seconds after his introduction.
The champion started in the manner expected of it as David Silva darted in behind and delivered a perfect cut-back for De Bruyne to apply a simple finish.
Provider should have turned goalscorer on the half-hour mark but David Silva poked across the face after Raheem Sterling wriggled free in the box.
A subdued atmosphere gave way to concern when centre-back Laporte was forced off after attempting a challenge that earned him a booking.
But striker Aguero lifted the mood in the 42nd minute, cushioning De Bruyne's pass and emphatically capping a classy team move.
Fernandinho had replaced Laporte in City's defence and positioned himself well to nod away Leandro Trossard's scuffed, close-range finish shortly after the restart.
Aguero offered no such mercy, brilliantly curling beyond an outstretched Mat Ryan to complete his brace in the 55th minute.
City moved back down the gears after wrapping up three points but there was time left for the two-goal Argentina star to add an assist to his impressive outing.
Aguero gathered Martin Montoya's poor header and spotted Bernardo Silva, who picked out the bottom-right corner to complete the scoring in the 79th minute.
City's first assignment after the international break is a trip to Norwich City on 15 September (AEST). Brighton entertains Burnley on the same day.