The point was enough to lift the Terriers off the foot of the table but they remain winless at the John Smith’s Stadium since the end of February, while the Lions are still searching for their first victory on the road since March.
The visitors later finished the game a man down after Shane Ferguson was sent off for two bookable offences in the second half.
An even start to the game, with half-chances for either side, came to life in the 24th minute, just two minutes after Millwall had carved out the best opportunity up until that point, with Jed Wallace inches wide with a low curler after turning Tommy Elphick inside the box.
A failed clearance from midway inside Millwall’s half on the left-wing sprang off Elias Kachunga and into the path of Karlan Grant. The striker then surged into the area before teeing up Campbell for a sidefoot finish from 10 yards for his first goal for the club.
The goal galvanised the Terriers, who enjoyed a purple patch that resulted in a Grant header saved by Bartosz Bialkowski and a flying headed effort from Campbell that just cleared the angle of bar and post.
Five minutes from the break, though, Millwall fortuitously clawed their way back into the game, with Grabara hero and then villain in the space of 30 seconds.
The 20-year-old Polish goalkeeper, on loan from Liverpool, produced a sensational fingertip stop to nudge over the bar a raking 30-yard strike from Ryan Leonard that moved through the air.
But from the Shane Mahoney corner that followed, Grabara made a complete hash of his attempted catch, with the ball almost dropping over the line only for Smith to intervene and help it on its way from less than a yard out for his third goal of the season.
After Mahoney curled over the bar a 22-yard free-kick early in the second half, following a nasty clash of heads between Jaden Brown and Smith, the home side again took the game to the visitors.
Two penalty shouts were rightly turned aside by referee Jeremy Simpson despite strong appeals for both from the Town players before the official was forced to reduce Millwall to 10 men in the 80th minute.
Ferguson was given his marching orders for two fouls on 57th-minute substitute Adama Diakhaby, the second of which was half a yard outside the area.
From the resultant free-kick, Diakhaby was inches away from curling home what would have been the winner, and despite their man advantage late on Town were unable to make a further breakthrough.