Defeat to Manchester City in their penultimate group-stage match meant PSG were guaranteed to finish in second place in Group B, but Brugge needed a win to confirm their place in the Europa League.
Yet it was the hosts who started by far the strongest with Mbappe scoring twice in the first seven minutes.
First, the France international coolly side-footed home from close range to become the youngest player to reach 30 goals in the Champions League, at 22 years and 352 days old, before doubling his tally for the night with a stunning volley from an Angel Di Maria dink over the top.
Messi netted his first of the game on the 38 minutes with a curling effort from the edge of the box, having previously been denied by Brugge goalkeeper Simon Mignolet.
Brugge threatened at the start of the second half and were rewarded with a goal Mats Rits reduced the deficit on 68 minutes, but Messi got a fourth for PSG from the penalty spot 14 minutes from time.
"We took this match seriously and we delivered a complete performance,'' Mbappe said. "We can still improve. The bottom line is that we need to manage our weak times better. We have weak times, which are maybe much too weak.''