Newcastle Falcons have one foot in the Amlin Challenge Cup quarter-finals thanks to captain Jimmy Gopperth's late conversion.
Fly-half Gopperth completed Newcastle's impressive second-half comeback by adding the extra points to Josh Afu's try, seven minutes from time, to snatch a crucial away victory at Stade Municipal.
The result stretches the Falcons' lead at the top of Pool Five to seven points over Montauban, who play on Saturday, before the final group matches next week.
Newcastle know victory over Italian minnows Petrarca at Kingston Park next weekend will guarantee their place in the last eight of the Challenge Cup for the fifth year in a row.
However they were made to work hard for the victory against an Albi team despite their lowly position in the French championship.
Penalties from Gopperth and Albi's Blair Stewart, a last-minute replacement at fly-half before kick-off, saw the teams level 6-6 at half time.
However a try swiftly after the break by replacement Yogane Correa handed Albi a lead they would hold onto until late on. Stewart cancelled out Gopperth's third penalty before flanker Afu finished a blistering Falcons attack to level the scores 14-14 ahead of Gopperth's conversion.
Connacht qualified for the quarter-finals of the Challenge Cup for the second year in succession after beating nearest rivals Montpellier 20-10 at the Galway Sportsground.
Only two points separated the teams in Pool Two before the tie but the Irish province maintained their unbeaten record thanks to second-half tries from Liam Bibo and Fionn Carr.
A brace of penalties from the boot of fly-half Ian Keatley handed Connacht a 6-3 lead at half-time in a closely fought contest at wind-swept Galway.
But Bibo burst through on 57 minutes before wing Carr followed nine minutes later to settle the tie. Keatley converted both before Mamuka Gorgodze touched down in the final minute for the French team. However their failure to gain a losing bonus point meant Connacht cannot be passed for top spot in the group.
Connacht travel to Madrid next week bidding to clinch top seeding and with it a guaranteed home draw in the quarter-finals.
Castres fly-half Thomas Bouquie scored one of his team's seven tries in an easy 47-0 victory over Roma at Stade Jean Pierre-Antoine. Bouquie added six conversions to finish with 17 points though Castres cannot catch Saracens to qualify from Pool Three.
Finals Edition: Listen to the best guide to the European Rugby Cup Finals weekend in Dublin, which sees Leinster Rugby take on Stade Francais Paris at the RDS on Friday night in the Amlin Challenge Cup Final and then ASM Clermont Auvergne tackle Toulon in an all-French affair at the Aviva Stadium on Saturday.