The Terriers were forced to come from behind after going 2-0 down at The McAlpine Stadium, but they fought back and a late strike from Rob Edwards saw them through.
After losing 2-1 in the first leg, Lincoln started strongly and took the lead after 38 minutes when Richard Butcher looped the ball in from the edge of the area after Paul Rachubka had fumbled.
Less than 60 seconds later and the home fans were stunned when Mark Bailey broke clear and lashed the ball past Rachubka to make it 2-0 at the interval.
Huddersfield pressed in the second half and were incensed when referee Mike Pike did not award them a penalty for an apparent handball by Ben Futcher from Efe Sodje's header, but not long after they were given a spot kick when Jamie McCombe was adjudged to have tripped Andy Booth.
Danny Schofield stepped up and stroked the ball home to make the scores level.
The game seemed destined for extra time, but with just seven minutes left Edwards became the hero as he picked up the ball on the edge of the area and hammered the ball past Alan Marriott in the visitors' goal.
Rachubka then denied Simon Yeo from close range as the Lincoln striker looked certain to force the game into extra-time. Huddersfield will now meet the winners of the Mansfield-Northampton clash in Cardiff's Millennium Stadium on Bank Holiday Monday.
Click below for match summary:
Huddersfield Town 2-2 Lincoln City (4-3 agg)
