Substitute Asamoah sets up Schalke win
Asamoah came on in the 58th minute and broke the deadlock for the hosts eight minutes later when he headed home Lukas Schmitz's cross.
Peru striker Jefferson Farfan also struck in stoppage time, converting a penalty for his fourth league goal of the season as Schalke hit back after losing their two previous home games.
Eintracht, who have now lost two in a row, had Pirmin Schwegler sent off in the 86th minute for a second bookable offence.
Felix Magath's Schalke climbed to third with 16 points from eight games, one point behind Hamburg SV and Bayer Leverkusen.