Accies were first to attack, and the pint-sized Spaniard Juanjo wasted a glorious chance in the fourth minute as he met a Mark Gilhaney cross on the six-yard line. The former Hearts player, however, fired over the bar with the goal at his mercy.
Assistant manager Stuart Balmer almost put through his own net as he tried to clear a Dundee corner minutes later, but thankfully for the centre-half his goalkeeper Dave McEwan displayed stunning reflexes to keep out the header.
Hamilton's Steven Thomson sent over a tempting lofted cross on the half hour mark, and Scott Tunbridge found himself with acres of space in which to pick his spot but the striker headed wide, much to the consternation of the home crowd.
Thomson was involved again two minutes later when he got on the end of an Alex Neil corner. The midfielder's header looked net bound only for Scott Robertson to pop up on the line and clear the ball to safety.
Accies should have taken the lead immediately after the restart when Brian Wake was played straight through on goal by Juanjo, but the striker inexplicably fired into the side netting when the goal was gaping.
Dundee's Kevin McDonald sent pulses racing in the 51st minute when he got on the end of a Simon Lynch cross. The winger's effort clipped the top of the bar, much to the relief of the home support.
Wake proved that hitting the woodwork was easier than hitting the back of the net in the 64th minute when his header from a Gilhaney cross crashed off the far post and out to safety.
The last chance of the match fell to Dundee's Paul Dixon, who crashed a 30-yard free-kick in the final minute only to see his netbound effort superbly parried by the impressive McEwan.
The replay at Dens Park looks set to be played on March 9 and covered live by Sky Television.