The reigning champions were held to a goalless draw by Lille last time out and struggled to find their stride again in Wednesday's clash at the Parc des Princes prior to a late flurry of goals.
Timothee Pembele's first strike for the club in his fifth appearance got PSG off the mark after 18 minutes, but it took until 11 minutes from time for Mbappe to add a second from a few yards out.
Substitutes Idrissa Gueye and Moise Kean then joined the scoring as Thomas Tuchel's men picked up a third league win in seven outings, although they end the year in third place a point behind Lyon and Lille, who both won elsewhere.
Strasbourg had won their previous two away games without conceding and would have taken the lead again if not for Keylor Navas' near-post save to deny Jean-Ricner Bellegarde.
But it was PSG who edged in front seven minutes later through Pembele's close-range finish after Eiji Kawashima parried Angel Di Maria's shot into the teenage defender's path.
Kawashima was almost at fault for another goal shortly before half-time, the visiting goalkeeper pushing Rafinha's long-range attempt into the air before recovering to scoop it off the line.
The lively Rafinha flashed a deflected shot just wide in a second half that PSG controlled without truly shaking off their opponents until Mbappe converted Di Maria's squared pass in the 79th minute.
Strasbourg heads dropped at that point and Gueye added a third with a fine swerving effort from outside the box, before fellow substitute Kean - on the field for just seven minutes - fired in after Marco Verratti was thwarted by Kawashima.