Smith's penalty sees Quins eliminate La Rochelle, Bordeaux secure top seeding
Earlier, Louis Bielle-Biarrey scored an opportunistic late try to complete his hat-trick and secure a 27-15 victory for Bordeaux-Begles at Bristol that earned them top spot in Pool 4.
La Rochelle needed only a losing bonus point to book their place in the last 16 at fellow two-time winners Leicester's expense but were undone by a late Quins flourish.
The 2022 and 2023 winners were pushing for a clinching score in the final 10 minutes when level at 17-17, only for Quins to burst upfield and break their hearts.