The summer signing from Wigan's thunderbolt from 30 yards proved to be the difference between the two sides as the Tigers won what was a low-key affair at London Road
The summer signing from Wigan struck midway through the first half, rifling a powerful drive into the roof of Bobby Olejnik's net from 30 yards, to give the newly promoted side the lead with his first goal in a Tigers shirt.
However, things could have been very different for Darren Ferguson's side had Tyrone Barnett not the hit post from a yard out moments before Figueroa's goal, after Steve Harper dropped a cross at the forward's feet, presenting the 27-year-old with an open goal.
After a slow start to the game, the Tigers, who included former Boro players George Boyd and James Chester in their starting line-up, began to take control and could have taken the lead inside the first 10 minutes.
Boyd's low cross found Sone Aluko on the edge of the area but a poor first touch from the former Rangers man allowed Peterborough, who start their League One campaign against Swindon Town on Saturday, to clear.
At the other end the Posh had a chance to take the lead themselves through Emile Sinclair but the 25-year-old's tame effort was well saved by Harper.
Despite inspirational playmaker Lee Tomlin showing moments of magic for the Posh, it was Hull who should have doubled their lead just after the half-hour mark, Danny Graham heading over at the near post when well-placed following Ahmed Elmohamady's floated corner.
And when Tomlin limped off moments later, Peterborough's chances of getting anything from the game faded as they began to sit back and allow their Premier League opponents to attack.
A flurry of changes from both sides slowed the tempo of the game after the interval as Hull remained in control, continuing to provide a threat through set-pieces, but poor delivery let Steve Bruce's side down as they struggled to double their advantage.
After being introduced to the action on the hour, substitute Joe Dudgeon proved to be a constant threat down the left for the Tigers, with a series of dangerous-looking crosses being whipped into the box but Peterborough held firm, heading the ball clear at each attempt.
With 20 minutes to go, Hull thought that they had succeeded in doubling their lead when Nick Proschwitz's glancing header floated in at the far post after he connected with Robbie Brady's right-footed cross, only for the German striker to be denied by the offside flag.
Joe Day had to be alert to push away Brady's driven free kick moments later, having rarely been troubled since being introduced to the action at half-time.
And, with the Posh defence remaining on top until the final whistle, Hull limped over the finish line as Figueroa's thunderbolt of a strike, worthy of deciding any game, proved to be the match-winner.