Marshall converted nine minutes after the interval following a contentious decision from referee Mike Jones.
Thomas Ince wasted Blackpool's best chances while former Scotland international Barry Ferguson rattled a post.
Foxes winger Lloyd Dyer looked dangerous early on and his second-minute cross was blocked and turned behind by the Blackpool backline with David Nugent and Jamie Vardy lurking.
Minutes later, former Stoke wideman Marshall found space on the right to play in summer-signing Vardy, who forced Matt Gilks into an instinctive save with his legs.
Nigel Pearson's men were threatening from both wings and Marshall's blocked shot rebounded to Danny Drinkwater for the former Manchester United youngster to test Gilks from the edge of the box.
Marshall's curling effort was then repelled by Gilks and the Blackpool number one had to get down quickly to again deny Marshall from a 25-yard free-kick.
Ian Holloway's table-topping Seasiders offered little going forward in the opening stages before Gary Taylor-Fletcher let fly with a long-range effort which swung wide of Kasper Schmeichel's goal.
And, despite being second best for the majority of the opening period, the visitors should have gone in front three minutes before the interval.
Taylor-Fletcher was given space to turn outside the Foxes' box and slip through top-scorer Ince but the 20-year-old wasted the opportunity to grab his fifth goal of the season.
Blackpool captain Ferguson then went even closer in first-half stoppage time as he superbly controlled Taylor-Fletcher's chipped pass to strike a left-footed effort which rebounded off the right-hand post with Schmeichel beaten.
City striker Nugent had the ball in the back of the net four minutes after the restart, only for it to be correctly ruled out for offside.
Moments later home fans voiced their displeasure as a penalty appeal was waved away after Neal Eardley appeared to bring down Dyer.
But on 53 minutes referee Jones was pointing to the spot when Vardy was adjudged to have been brought down by Tiago Gomes and the lively Marshall converted into the top left-hand corner.
On-loan Wigan striker Nouha Dicko was denied a penalty at the other end after going down under Paul Konchesky's challenge while Ince threatened with a snapshot which flew over from an acute angle.
Dyer almost doubled the hosts' lead 19 minutes from time but his powerful close-range drive struck the face of Alex Baptiste on the line.
Ince was presented with a golden chance to grab an equaliser four minutes from the end but he shot wide with the outside of his left foot when well placed to score.