Shaun Maloney claimed his first goal for Wigan from the penalty spot in the first half, only for Luis Suarez to equalise early in the second half.
But Caldwell gave Wigan a 2-1 lead just after the hour as Liverpool surely saw their lingering hopes of a top-four finish disappear.
Whatever successes Dalglish enjoys in cup competitions this season, this defeat must rank as the low point of his reign.
Wigan struck a sensational opening goal from the penalty spot just beyond the half hour, after Liverpool's early dominance of possession had failed to generate a single clear-cut chance.
James McCarthy charged down Jordan Henderson's attempted clearance and allowed Caldwell to chip the ball forward into the Liverpool area where, as Victor Moses tried to connect with a shot, a high boot from defender Martin Skrtel caught him in the face.
Referee Lee Mason had no hesitation in awarding the penalty and, after a three-minute delay while Moses received treatment, Maloney calmly strode up to place his spot kick into the bottom left-hand corner.
Maloney's composure was in stark contrast to that shown by Liverpool, who were seeking to improve upon a dreadful home league record of just five wins from their 14 games prior to Wigan's visit.
For all their possession, however, it was not until the 24th minute that they created a chance of note, when Stewart Downing chased a through ball from Suarez and sent a powerful shot flying just wide of the right-hand post.
The penalty dramatically increased Liverpool's urgency and, finally, after 40 minutes the Wigan goalkeeper Ali Al Habsi was forced into his first save.
Suarez gathered a short pass from Steven Gerrard on the edge of the area, falling over but rising to turn and drill a right-foot shot towards goal with Al Habsi diving smartly to his left to keep it out.
In the four minutes of first-half added time, Dirk Kuyt and Suarez also linked well to put through Gerrard, whose left-foot near-post effort was again well saved by Al Habsi.
Dalglish brought on forward Andy Carroll at the interval, a switch that apparently breathed an instant improvement into his team, who drew level within two minutes of the restart.
Kuyt laid off a neat pass to Gerrard, who timed his through ball to perfection, delivering it to the six-yard line, where the on-rushing Suarez swept it convincingly past Al Habsi.
Suarez, growing in confidence, sent a shot curling over from 20 yards before he appeared to have put Liverpool ahead on 52 minutes.
Skrtel rose powerfully to head a Gerrard free-kick at the far post and Suarez celebrated after forcing the ball over the line, but replays clearly showed that the Uruguay international had handled.
To add to Suarez's woe, he was also cautioned for the infringement.
Liverpool's relief at being level was short-lived as just after the hour they conceded a second goal which, like the first, came very much against the run of play.
Carroll headed a free-kick out of the Liverpool area and James McArthur responded with a 20-yard shot that struck Carragher on the arm and fell kindly for Caldwell.
The defender neatly changed feet, leaving his marker Carroll on the floor, before beating Jose Reina with a clinical right-foot finish from eight yards.
Suarez placed a free-kick from the edge of the area directly into the Wigan wall and despite a promising cameo from highly regarded teenage substitute Raheem Sterling, there was to be no way back for Liverpool.
Wigan upset Liverpool 2-1 to boost survival hopes
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