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.
Tom Lawday scored in the corner with eight minutes left and after Smith converted, La Rochelle trailed by seven points.
That would have been enough to earn the losing bonus point but Smith's last-gasp penalty denied them that and sent them into the Challenge Cup knock-outs.
La Rochelle had drawn first blood on 11 minutes with a try from wing Davit Niniashvili but Quins exploited a yellow card to French prop Uini Atonio to score through backs Cadan Murley and Tyrone Green for a 17-7 lead.
However, Quins had fly-half Smith binned in the second half and La Rochelle took advantage to draw level through unconverted tries by former England wing Jack Nowell and scrum-half Thomas Berjon.
But Smith's return to the field proved costly for the French side, while victory ensured Quins will play at home in the last 16.
Bielle-Biarrey and Todaro trebles
In southwest England, hooker Gabriel Oghre put hosts Bristol on the board first but wing Bielle-Biarrey grabbed two tries and centre Nicolas Depoortere one as Bordeaux took a commanding 17-5 lead into the break.
South African centre Benhard Janse van Rensburg's try closed the gap with Sam Worsley converting and adding a penalty to bring the Bears to within five points of the reigning champions.
But Bielle-Biarrey's quick reflexes and dart of speed got him first to a loose ball to seal the win that guarantees Bordeaux will finish the pool stages as one of the top two seeds, giving them home advantage through to the semi-finals.
Last season's beaten finalists Northampton leapfrogged Bristol into second place in the group as Italian wing Edoardo Todaro scored a hat-trick of first-half tries in an entertaining 43-28 victory over Scarlets.
The Welsh region had taken a surprise lead through tries from Ryan Elias and Archie Hughes but once the Saints juggernaut chugged into gear, they seemed to be running away with it.
Ollie Sleightholme and Craig Wright added to Todaro's hat-trick but Scarlets bounced back through tries from Sam Costelow and Jac Davies to leave them within a converted try of the victory they needed to stay in the tournament.
But Anthony Belleau scored a penalty and replacement flanker Callum Chick added a try to eliminate Scarlets and send South Africans Bulls into the last 16.