Edinburgh failed to recover from a horror start to their European Challenge Cup quarterfinal as La Rochelle triumphed 32-22 at Murrayfield.
Visiting hooker Jeremie Maurouard capitalised on two driving mauls in the opening 12 minutes and the visitors added two more first-half tries after Phil Burleigh's counter to move 19 points ahead.
Ross Ford and Hamish Watson crossed and Edinburgh cut the deficit to four just after the visitors had a man sent to the sin-bin.
The Scots had won their last 11 home European games with six Top 14 teams among their victims but the French league leaders stood firm.
Edinburgh came into the game on the back of six consecutive defeats but they had saved their best form for Europe all season, winning one more game in the Challenge Cup (five) than in the Guinness PRO12 so far on their way to topping their pool.
But it was their league form that was on show for the 5,489 fans early on.
Sam Hidalgo-Clyne prevented an even earlier try than La Rochelle's sixth-minute opener when he tackled Pierre Aguillon into touch two metres out but the hosts shot themselves in the foot when Blair Kinghorn miss-kicked out of play.
The visitors took full advantage with the first of two near identical tries from five-metre lineouts with Brock James' kicks making it 14-0.
Edinburgh settled down quickly and Chris Dean's burst of pace threatened to expose a gap in the French defence but he delayed his pass.
The hosts kept the pressure on with a penalty into the corner and Burleigh eventually worked his way over the line on the opposite flank midway through the half, with Jason Tovey kicking over from the touchline.
But the good work was undone by another poor piece of play from Kinghorn. Scrum-half Arthur Retiere emerged from a group of players on the left wing near the halfway line and wriggled past a lacklustre challenge from the Edinburgh full-back to continue all the way.
Edinburgh again refused to capitulate but Tovey was stopped forcefully near the line and they failed to make the most of two penalties kicked into the corner before more trickery from Retiere sent Steeve Barry under the posts.
The hosts got a lifeline when Ford quickly got the ball back after his lineout throw and easily brushed off Barry to go over near the corner. Tovey failed to cut the 14-point deficit further with the last kick of the half.
The next try was crucial and Edinburgh set about getting it. Watson and Kinghorn were held up but Hodge's side kept pushing and Watson crossed after an excellent offload from Viliame Mata.
After a more cautious period of play, Edinburgh broke free in the 64th minute with the help of Watson's kick and Lekso Kaulashvili took a yellow card for his team by hauling Damien Hoyland back without the ball as the winger looked set to break for a try on the 22-metre line. Duncan Weir kicked the resulting penalty to reduce the arrears to four.
The progress was soon cancelled out by a James penalty and Edinburgh could not capitalise on their man advantage, with their best spell of pressure ending abruptly with Simon Berghan's sloppy pass.
With the visitors back to 15 men, James kicked another late penalty to put the tie beyond doubt.
