The result saw the Cumbrians slip to 10th in the table, but they remain just one point outside the play-off places with two games remaining.
Carlisle, 2-0 down after 25 minutes, were level before the interval and led through Reggie Lamb before Smith had the final say.
Carlisle midfielder Jamie Davitt fired against the post and Jamie Proctor put a good chance wide before Crawley took the lead in the 11th minute.
Leading marksman James Collins opened the scoring in superb style by smashing a tremendous shot into the top corner from 20 yards.
Collins was on target again after 25 minutes from the penalty spot, sending Mark Gillespie the wrong way after the goalkeeper had brought down the striker.
Striker Jabo Ibehre, put clean through by Danny Grainger, reduced the deficit four minutes later with his fourth goal in four games.
Crawley keeper Glenn Morris was then hurt as Ibehre put the ball in the net and had to be replaced by Yusuf Mersin.
Carlisle were level three minutes before the break when Proctor, on loan from Bolton, struck with a bullet header following a Gary Liddle cross.
United seized the lead on the hour through Lambe, who clipped the ball past replacement keeper Mersin after latching onto Proctor's cross.
Josh Payne fired just wide late on for Crawley and Collins also headed over before the hosts levelled in the second minute of stoppage time when Smith fired in following a pass from Joe McNerney.
Match report supplied by the Press Association.
Match ends, Crawley Town 3, Carlisle United 3.
Second Half ends, Crawley Town 3, Carlisle United 3.
Attempt missed. John O'Sullivan (Carlisle United) right footed shot from outside the box misses to the right.
Goal!  Crawley Town 3, Carlisle United 3. Jimmy Smith (Crawley Town) right footed shot from the right side of the box to the bottom right corner. Assisted by Joe McNerney following a set piece situation.
Josh Payne (Crawley Town) wins a free kick in the defensive half.
Foul by Ben Tomlinson (Carlisle United).
Hand ball by Josh Payne (Crawley Town).
Substitution, Carlisle United. Shaun Brisley replaces Reggie Lambe.
Hand ball by Ben Tomlinson (Carlisle United).
Attempt missed. James Collins (Crawley Town) header from the centre of the box is just a bit too high following a set piece situation.
Delay over. They are ready to continue.
Delay in match Lewis Young (Crawley Town) because of an injury.
Lewis Young (Crawley Town) wins a free kick on the right wing.
Foul by Jabo Ibehre (Carlisle United).
Attempt saved. Josh Payne (Crawley Town) right footed shot from outside the box is saved in the centre of the goal.
James Bailey (Carlisle United) is shown the yellow card for a bad foul.
Jordan Roberts (Crawley Town) wins a free kick in the defensive half.
Foul by James Bailey (Carlisle United).
Substitution, Carlisle United. John O'Sullivan replaces Jamie Devitt.
Delay in match Reggie Lambe (Carlisle United) because of an injury.
Corner,  Carlisle United. Conceded by Josh Yorwerth.
Attempt missed. Luke Joyce (Carlisle United) right footed shot from outside the box misses to the left.
Attempt missed. Josh Payne (Crawley Town) right footed shot from outside the box misses to the left.
Foul by Jordan Roberts (Crawley Town).
Gary Liddle (Carlisle United) wins a free kick on the left wing.
Jordan Roberts (Crawley Town) wins a free kick in the defensive half.
Foul by Reggie Lambe (Carlisle United).
Substitution, Carlisle United. Ben Tomlinson replaces Jamie Proctor.
Lewis Young (Crawley Town) wins a free kick on the left wing.
Foul by Jamie Proctor (Carlisle United).
Corner,  Crawley Town. Conceded by Macaulay Gillesphey.
Reggie Lambe (Carlisle United) is shown the yellow card for a bad foul.
Enzio Boldewijn (Crawley Town) wins a free kick in the defensive half.
Foul by Reggie Lambe (Carlisle United).
Substitution, Crawley Town. Jordan Roberts replaces Kaby.
Josh Yorwerth (Crawley Town) wins a free kick in the attacking half.
Foul by Jamie Proctor (Carlisle United).
Attempt missed. Jimmy Smith (Crawley Town) left footed shot from the right side of the box misses to the right.
Foul by Enzio Boldewijn (Crawley Town).
Danny Grainger (Carlisle United) wins a free kick on the right wing.
A stoppage-time equaliser by captain Jimmy Smith denied Carlisle a crucial victory in their play-off challenge as Crawley salvaged a draw at home.