Kapur totalled five-under 283 at the club in Golf de Geneve.
Kapur began well with two birdies in first five holes, but then lapsed into errors with three bogeys between sixth and ninth, even though he had an eagle on eighth. Two birdies on 13th and 15th again seemed to have put him back on rails, but bogeys on 16th and 18th saw him finish at 71.
Jens Dantorp captured his maiden Challenge Tour title at the Rolex Trophy and ensured that the trophy stayed in Swedish hands following Kristoffer Broberg's victory last year.
After closing with a trio of pars to sign for a round of 70 and better by one the clubhouse target of 17 under par set by Spain's Adrian Otaegui, Dantorp faced an anxious wait to see if Lima - playing in the group behind - could birdie the last to force a play-off.
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Lima's approach pitched close to the pin, but agonisingly rolled back down the slope to leave the Portuguese facing a 30-foot putt to take the elite 42-man tournament into extra time.
Dantorp receives a brand new Rolex watch and a cheque for Euro 26,000, which moved the Swede 27 places up the Rankings to 11th and within sight of joining Broberg on The European Tour next year.