Borders 21-26 Connacht
Gareth Morton leads an attack for the home side
The Borders' dismal start to the season continued when they were bundled out of the Celtic Cup at the first hurdle by Connacht at Netherdale.
After two heavy defeats in the league, the home side looked on course for a much-needed win as they led with just four minutes remaining.
But they threw away all the good work by handing Mark McHugh two penalty chances, which he gleefully snapped up.
Borders' preparations had been rocked when veteran lock Doddie Weir was forced to pull out of the team before the kick-off with a bout of flu.
Then scrum-half Chris Cusiter was taken off with a wrist injury in the opening minute of the match.
Weir was replaced by Scott MacLeod, while veteran Gary Armstrong came off the bench to fill the number nine berth.
Borders shrugged off the double setback to break the deadlock with a Gareth Morton penalty.
But the home team were set back on their heels as former Ireland international Eric Elwood bagged a hat-trick of goals in the space of six minutes.
The penalty exchanges continued with another strike by Morton.
Another flurry of kicks, including an Elwood drop-goal, took the score to 9-15 - but then the Borders carved out a great try, despite having Campbell Feather in the sin-bin.
Wing Andy Turnbull raced into the Connacht half and claimed the first five-pointer after winning the race to his own chip.
Craig Moir then marked his return from injury with another try just after the restart, Morton adding the goal to give Borders a six-point edge.
Mick McCarthy hit back with a touchdown for Connacht, only for McHugh's conversion to hit the post.
But the Connacht replacement had the last say with his two late strikes to earn the Irishmen a daunting quarter-final away to the Scarlets at Stradey Park.
The Borders: G Morton, C Moir, J Stuart, K Utterson(captain), S Paterson, C Laidlaw, C Cusiter, K Todd, R Ford, G Cross, D Weir, C Stewart, A Rennick, D Kane, C Feather.
Replacements: S Scott, C Dunlea, S MacLeod, T Walker, G Armstrong, I Fairley, C MacRae.
Connacht: D Hewitt; M Mostyn, D Yapp, T Allnutt (c), T Robinson; E Elwood, C O'Loughlin; W O'Kelly, J Fogarty, F Boiroux; M McCarthy, A Farley; P Neville, J O'Sullivan, M Carroll.
Replacements: M Uijs, R Hogan, M Swift, T Carter, M Walls, S Moore, M McHugh.