City took the lead on 34 minutes when Aguero flicked on Kevin De Bruyne’s in-swinging cross.
Karl Darlow saved superbly from De Bruyne before the interval and touched Raheem Sterling’s shot on to the post.
But Aguero struck again from the penalty spot after Sterling had been felled by Javier Manquillo.
Jacob Murphy reduced the arrears on the break with a dinked 67th-minute finish.
Aguero then registered his 138th PL goal and his seventh hat-trick in the competition after a bamboozling, late run by Leroy Sane.
City restored their 12-point lead at the top. The Magpies lie 15th.
Man City: 31 Jan v West Brom (H)
Newcastle: 31 Jan v Burnley (H)