Posh had lost 16 of their 18 away games this season ahead of their daunting trip to the south coast.
But Marriott’s strike on the half-hour, cancelled out by Ryan Christie effort in the second half, turned the form table upside down.
Bournemouth boss Scott Parker was free to take his place in the dugout while he awaits punishment from the FA for his sending off in Saturday’s 2-1 defeat at Preston.
Parker handed January signing Siriki Dembele a starting berth against the club he left for £1million in January.
Posh made six changes from Friday’s defeat at Huddersfield as manager Grant McCann tried to arrest their dreadful away run.
McCann’s last win in charge of Hull was at the Vitality Stadium.
Bournemouth, looking to bounce back from Saturday’s defeat at Preston, dominated possession in the first half but were wasteful in front of goal.
The hosts carved the first of numerous good chances after only two minutes.
Posh old boy Dembele cut in from the left before picking out Christie on the edge of the penalty area and the Scotland international curled his shot wide.
Marriott gave the hosts a scare a minute later by racing in behind the Bournemouth defence and shooting into the arms of Mark Travers.
Bournemouth came close again in the 10th minute when lovely interplay between Todd Cantwell and Dominic Solanke resulted in the latter failing to hit the target.
Defender Nat Phillips then blazed over from a Christie corner as the Peterborough goal continued to lead a charmed life.
Philip Billing should have done better in the 27th minute when a Christie cross was cushioned down by Solanke and the Dane smashed his shot high over the crossbar.
The home side were made to pay for their wastefulness when Joe Ward slid his pass through the legs of Lloyd Kelly for Marriott to fire into the bottom corner.
Bournemouth’s first shot on target came five minutes before half-time when Billing’s effort was saved at the near post by David Cornell.
Kelly then headed over from Christie corner in first-half stoppage time.
But it was 1-1 seven minutes after the re-start as Christie finished neatly after driving into the penalty area.
It was the 70th goal Peterborough had conceded in the league this season but the closest Bournemouth came to a winner was Billing’s curling effort wide.
In fact, it needed a heroic block from Kelly three minutes from time to keep out Ward’s goal-bound effort and deny Peterborough a dramatic late winner.
The point moved Bournemouth back into second place but still left Parker frustrated.