Bottom placed Luton, recovering from being docked 30 points at the start of the season, and Bournemouth, who were penalised 17, battled furiously without being able to find a winner.
Hollands put Luton ahead with a soft goal after only 11 minutes.
Luton striker Sam Parkin headed across the face of the Bournemouth goal and Hollands turned it past his own goalkeeper while attempting to clear.
But Bournemouth were level in the 29th minute when Hollands seized on a desperate clearance to fire home from 20 yards with the aid of a deflection.
Chances at either end were rare in a match neither side could afford to lose.
Steve Fletcher shot over the bar from a pass by Jake Thomson, but it was Luton who had the best opportunity to collect the points.
As Luton's pressure mounted in the closing stages, a fierce shot from Kevin Gallen was blocked on the line by Bournemouth substitute Alan Connell.
In the last minute, Luton goalkeeper Conrad Logan raced from his goal to save at the feet of substitute Jeff Goulding.
Luton manager Mick Harford took off Ian Roper soon after the defender had been booked for a foul in the 52nd minute and then replaced the hard-working Kevin Nicholls in a bid to get a grip in the middle of the field.
Harford's counterpart, Eddie Howe, also gambled near the end sending on Connell and Goulding in place of Fletcher and Sammy Igoe, but Luton held on.
Luton had Nicholls and Asa Hall booked for fouls by Premier League Referee Steve Bennett, who showed yellow cards in the second half to Bournemouth central defenders Jason Pearce and Shaun Cooper.