Ross County outplayed Clydesdale Bank Premier League opponents Hamilton for long spells in a thoroughly deserved victory in this Co-operative Insurance second-round tie at Victoria Park.
Man of the match Paul Di Giacomo opened the scoring just after the half hour-mark with a fine opportunist strike and Richard Brittain increased the lead seven minutes into the second half with a decent strike from 15 yards.
Accies got a consolation in injury time when Simon Mensing drilled the ball low into the net.
Hamilton had the first effort on goal in the fifth minute when Mensing played a neat one-two with Leon Knight but County goalkeeper Michael McGovern got down well to smother Mensing's drive.
There was a chance at the other end seconds later when a deep cross from Iain Vigurs found Brittain at the back post but, with the goal at his mercy, he ballooned his shot over the crossbar.
County were looking dangerous in the early stages and they had another half chance in the 10th minute when Brittain flicked the ball on to Michael Gardyne but he hooked his shot well wide of target from 12 yards out.
The home side came close again in the 15th minute when Di Giacomo nipped in between Luis Rubiales and Mark McLaughlin and squared the ball for Gardyne but Martin Canning got there first to clear the danger.
The SPL side were only seen in patches and County kept pushing forward as Di Giacomo caused the Accies defence all sorts of problems.
The County forward got on the end of a four-man move and forced a fine save from Tomas Cerny, the ball broke to Vigurs who lined up Paul Lawson to drill a low shot just wide of the upright.
In a rare attack Hamilton's James McArthur tried a snap shot from 25 yards but it came off the stanchion behind the goal.
County deservedly took the lead in the 31st minute when Gardyne swung a ball in from the left and Brittain headed the ball against the crossbar but Di Giacomo latched onto the rebound to fire the ball into the net.
Gardyne was away from his marker a minute later but he overhit his pass inside with Di Giacomo in a good position.
Just on half-time Alex Keddie came up from the back to send a Brittain corner over the bar at the far post.
Accies were seeing a lot more of the ball at the start of the second half but it was County who doubled their lead in the 52nd minute.
Di Giacomo won possession in the middle of the park and his short pass to Stuart Kettlewell was swept across to Brittain who took one touch and hammered the ball low into the net from 12 yards.
Accies had a great chance to get back into the tie four minutes later when Marco Paixao had a clear sight of goal but McGovern made a brilliant point-blank save to keep him out.
Accies made a double substitution in the 63rd minute with JP Kissock and David Louhoungou coming on for Rubiales and Paixao.
But it was County who came close to adding to their score in the 70th minute when a Scott Morrison ball into the box was knocked on by substitute Martin Scott but Di Giacomo failed to turn the ball in at the back post - and Mensing's strike was too late to send County hearts fluttering.