As against Leinster last week, the Borders started very well, with blindside flanker Kelly Brown getting the touchdown after good work from the Borders pack on 15 minutes. Charlie Hore's conversion was quickly followed by a penalty to send them ten clear.
Playing with a strong breeze in the first half, tries from their captain and former Auckland prop Paul Thomson on the half hour and shortly thereafter from former Otago player and another from Hore, chasing his own kick ahead, gave The Borders a very healthy 22-3 lead, Elwood having slotted a penalty on 27 minutes.
Conor O'Loughlin got his reward for a sniping run just five minutes before the interval - key score improving the half-time score to 22-10 with the elements to come in the second half.
This became even more manageable with an early Elwood penalty in the new half. But Hore, fed by outhalf Ally Warnock, wrapped up The Borders' second bonus point of the season on 50 minutes with a try in the corner and restored the Scots' advantage to 14 points.
But Connacht finished strongly. Warwick fed winger Niall O'Brien to go in on 57 minutes. Although Elwood missed the convert, he did bag a penalty to reduce the deficit to six at 27-21 to The Borders.
A late Andrew Farley try gave Elwood what he must have felt was his last chance to win the match, but he missed the right to left attempt. But a Borders infringement on the deck gave him a final shot, with which there was to be no mistake.
Cue massive relief. And a certain sympathy for a Borders team that has been struggling manfully in trying conditions.