Tambwe took his tally for the season to nine tries, crossing twice in the second half to help Bordeaux-Begles book a tie with Champions Cup holders La Rochelle in San Sebastian next Saturday.
In the other semi-final, record 21-time champions Toulouse will play Racing 92 on Friday after they beat Stade Francais 33-20 in a Parisian derby.
Before kick-off in balmy conditions in Lyon, host broadcaster Canal+ said there would be no TMO during the match because of a technical issue linked to the TV truck.
The first controversy due to the problem came after six minutes as Matthieu Jalibert crossed for Bordeaux-Begles and referee Ludovic Cayre awarded the try despite television footage showing a knock-on from the fly-half.
The home side responded to lead 17-8 at the break as France winger Ethan Dumortier and Fiji centre Josua Tuisova responded to Jalibert’s early effort.
With half an hour to play there was just two points between the sides as Jalibert converted Mahamadou Diaby’s try to make it 17-15.
Diaby’s touchline effort was whistled by the home fans as the flanker seemed to lose control of the ball.
Tuisova hobbled off the field due to a knee issue with a quarter of an hour remaining before 26-year-old Tambwe and Lyon centre Josiah Maraku crossed to leave the score 25-25 with five minutes left.
Tambwe’s crucial intervention came with two minutes to go as he galloped 50 metres to score from a set-piece move and Jalibert added the conversion as Bordeaux-Begles secured a last-four spot with just their third away win of the season.
On Saturday, Perpignan avoided relegation for a second straight season by beating Grenoble 33-16 in a play-off at a sold-out Stade des Alpes.
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