The hosts had looked in control in the early moments, but their opponents struck the woodwork twice before the break.
It was a more fluent display from the Blues in the second half, though, and Marquis’ goal secured a deserved victory.
Danny Cowley made one change from the side that struck late to secure a point at Accrington the previous week.
Ryan Tunnicliffe returned to the starting line-up, with Joe Morrell the man to make way and dropping to the bench.
Former Fratton loanees Eoin Doyle – who helped secure the 2016/17 League Two title – and Lloyd Isgrove were both named in the Wanderers side.
There were impeccably observed remembrance tributes before the game, as both clubs paid their respects to those who made the ultimate sacrifice.
Pompey made the brighter start, dominating both possession and territory in the contest’s opening stages.
Ronan Curtis showed some tricky footwork before eventually being dispossessed in the box by Ricardo Almeida Santos.
The Republic of Ireland international then had to stretch to meet a Marcus Harness delivery and could only nod the ball wide.
And following great work on the right by Reeco Hacket, Will Aimson did well to clear before the ball could reach Marquis in the centre.
Curtis had the hosts’ best chance of the half on 25 minutes, but Joel Dixon got down well to deal with his effort.
Bolton then came back into the contest as the action progressed and a thunderous strike from Dapo Afolayan rattled the crossbar.
And Mahlon Romeo did brilliantly to clear a Nathan Delfouneso delivery and deny Doyle a simple finish.
Pompey were forced to make a change late in the half after Tunnicliffe got injured in a challenge with Afolayan.
The midfielder quickly signalled that he was unable to continue and was replaced by Louis Thompson.
There was time for one more chance for the visitors before the interval, as Declan John clipped the outside of the post from an acute angle.
Bolton Wanderers 0
Pompey regrouped at the interval and came out strongly again once the action restarted, with Sean Raggett heading a Hackett free-kick over.
But the deadlock was broken on 51 minutes, courtesy of a neat back-flick by MARQUIS and an eagle-eyed assistant.
Curtis collected the ball from Hackett on the left and sent in a low cross that the striker met with an instinctive finish.
Wanderers keeper Joel Dixon desperately tried to stop the ball from going in, but the linesman spotted that it had crossed the line.
The keeper did prevent Marquis from adding a second moments later, making a smart stop with his feet.
Pompey’s number nine was certainly busy and could not guide a Romeo cross on target before seeing a Thompson delivery taken off his head by Santos.
Curtis then waltzed his way into a shooting position, but opted to take on one defender too many and was eventually dispossessed.
Cowley made his second switch on 78 minutes, with Morrell taking over from Shaun Williams in the engine room.
And it was still the hosts looking the more likely to score again, although Curtis’ effort lacked the power to properly trouble Dixon after brilliantly bringing a Gavin Bazunu clearance under control.
The contest was not over, though, and Doyle reminded the hosts of that by nodding a Harry Brockbank cross against the top of the bar.
But the Blues were able to see out the closing stages with relative ease to ensure they earned a much-needed win.
Pompey (4-2-3-1): Bazunu; Romeo, Raggett, Ogilvie, Brown (c); Tunnicliffe (Thompson 40), Williams (Morrell 78); Harness, Hackett, Curtis; Marquis (Hirst 90+4)
Goals: Marquis 51
Subs not used: Bass, Freeman, Azeez, Jacobs
Bolton (4-1-4-1): Dixon; Isgrove (Brockbank 72), Santos (c), Aimson (Johnston 72), John; Williams; Delfouneso (Sheehan 56), Lee, Afolayan, Kachunga; Doyle
Subs not used: Gilks, Baptiste, Gordon, Thomason
Referee: Craig Hicks
Attendance: 16,231 (1,087 away fans)