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The Scottish visitors had led 22-3 after half an hour and looked on course to collect their first ever away win in the league but Connacht battled back and with hooker Steve Scott sin binned the home side snatched a late try and then – deep into injury time – Elwood slotted the winning penalty with the last kick of the game.
Charlie Hore collected the first of his two tries while Paul Thompson and Kelly Brown added one apeice as the Borders raced into an early lead with a strong wind behind them.
However the Irish province battled back and a Conor O’Loughlin try which Elwood converted saw them turn round 22-10 down.
Hore’s second try had the bonus point secured within ten minutes of the restart, but Niall O’Brien continued the comeback with Connacht’s second try on the hour and as the Borders defence began to falter Andrew Farley smashed over and although Elwood missed the conversion it set up the grandstand finish with Elwood ultimately the hero.