Winger Simon Baldry scored just three minutes into his first start after a long injury lay-off to help put Huddersfield Town into the Worthington Cup second round for the first time in three years.
Baldry, out for nine months, returned to the side and made an immediate impact by scoring from close range after Jon Stead's left wing cross was not cut out by the Darlington defence.
And the home side were 2-0 up 12 minutes later when Quakers defender Matt Clarke headed into a Kenny Irons cross into his own net.
Darlington recovered quickly from their mistakes and went on to boss the midfield action. They created a number of clear-cut chances but the Terriers' Australian goalkeeper Scott Bevan was in commanding form.
Bevan reacted swiftly in the 56th minute to keep out Mark Ford's fierce low drive and was up on his feet quickly to stop Ian Clark from putting away the rebound.
Three minutes later he brilliantly tipped over a long-range effort from Neil Maddison and in injury time the 6ft 6ins keeper parried a David McGurk header.
Town boss Mick Wadsworth was full of praise for the on-loan Southampton keeper afterwards. "He is a top-class keeper and he pulled off two great stops and that's what we brought him here for," he said.
"He kept us in it at crucial times and if we had conceded a goal it could have been hard work for us. "
Visiting boss Tommy Taylor was proud of the way his team shrugged off their early mistakes to produce a bright and attacking display.
"Playing a team in a different division means that we must give them respect and match them in every department but you cannot legislate for the kinds of mistakes we made.
"But I told the lads at half time to forget the mistakes and concentrate on their own performances. The stuck to their task but despite plenty of possession the goals just did not come."