Hull swept into an eighth-minute lead through Matty Fryatt's 11th goal of the season, but Leicester hit back with two superb long-range efforts from Dyer and Marshall in as many minutes.
Foxes midfielder Neil Danns was shown a straight red card in the 57th minute for his reckless challenge on Paul McKenna, but Leicester secured their fourth straight home league win against manager Nigel Pearson's former club.
Hull, beaten at home by Southampton on Tuesday night, saw their own play-off chances dealt another blow as they have won only one of their last eight league matches.
Leicester manager Pearson, who left Hull in November, stayed true to the side that drew 3-3 at Blackpool in midweek, while midfielder Corry Evans and winger Cameron Stewart returned for Hull.
Hull quickly put Tuesday night's home defeat to the leaders behind them with a fine opening goal in the eighth minute.
Midfielder Tom Cairney picked out Fryatt in the penalty area and the striker clipped a neat finish over sprawling Leicester goalkeeper Kasper Schmeichel from eight yards.
Evans then lashed a 25-yard shot wide for the visitors and Tigers striker Josh King forced Schmeichel into a terrific save with an angled drive from inside the area.
But two goals in as many minutes turned the first half on its head.
Leicester full-back Lee Peltier played the ball inside from the right to the edge of the area and Dyer drilled a low shot, first time, into the bottom corner.
The Foxes then surged straight back down the field from the restart and when David Nugent slipped the ball to Marshall 25 yards from goal, the winger unleashed an unstoppable shot into Hull goalkeeper Vito Mannone's top left-hand corner.
Neither stopper was troubled again until Marshall blazed another shot from outside the area over the crossbar just before half-time.
Leicester were dealt a blow 12 minutes after the restart when midfielder Danns was shown a straight red card by referee Nigel Miller for his dangerous tackle on Hull midfielder Paul McKenna.
Within six minutes Hull almost made their one-man advantage pay. Left-back Andy Dawson swung over a corner and central defender Hobbs rose to crash a superb header against the post with Schmeichel well beaten.
Hull poured forward in search of an equaliser, but Leicester went close to extending their lead through Danny Drinkwater's angled drive, which was well saved by Mannone before substitute, Sol Bamba rattled the post with a thunderbolt from 35 yards.
Dyer's thumping drive from 25 yards flashed inches past the post in the 87th minute as Leicester's 10 men finished strongly.
Hull defender Liam Rosenior fired a long-range shot straight at Schmeichel in the closing stages, but Pearson's side held on without further incident to climb five points adrift of the play-offs with eight games remaining.