Morison tucked home the opener in front of a crowd of 10,115 after just three minutes and Poleon was on hand to add a second four minutes from time to put the seal on a decent afternoon for the hosts, who open their Championship campaign at Millwall in seven days time.
A presentable attendance, with a noisy following from Dundee having travelled south of the border, saw a first half dominated by the hosts, who carried on from where they left off in a decent mid-week performance in beating Swindon.
It was the same line-up who started at the County Ground, minus Stuart Taylor, who took the field with number one Marco Silvestri afforded a nice reception when he lined up in front of the Kop for the first time.
In the event, the Italian keeper had next to nothing to do in the first half, with his only save being a routine one on the half-hour to stop Stuart Armstrong’s low shot, which was pretty token.
United, who played some patient probing football, with Michael Tonge at the heart of it, dovetailing well in the middle of the park with Tommaso Bianchi and Luke Murphy, bossed proceedings and were full value for their lead.
It arrived just three minutes in with good play down the right by Tonge saw him send over an inviting low cross following early pressure which was tucked away at the far post from close range by Morison.
Soon after, Callum Morris headed over when well placed following Chris Erskine’s corner, but it was a threatening moment in isolation for the visitors.
Rudy Austin then stepped forward before unleashing a rasping shot which was turned away by Radoslaw Cierzniak as Leeds went close to a second.
Tonge, after a bright opening, fired an effort wide in a quest to extend the Whites' lead on 17 minutes before Sam Byram teed up another who figured prominent in the opening twenty minutes in Bianchi, who saw his stinging shot crash against the woodwork.
It was all encouraging stuff from Leeds and appreciated by the fans who braved the rain to turn out in the sole pre-season fixture at Elland Road.
After Armstrong shot at Silvestri, Leeds assumed command again with Tonge shooting straight at Cierzniak before a quality move could - and perhaps - should have yielded another home goal.
Tonge fed Souleymane Doukara, who totally bamboozled Jarek Fojut down the right, lofting the ball over him before setting up Bianchi in front of goal, but he delayed, allowing Erskine to make a saving block.
Chances were at more of a premium on the restart, but United’s efforts to play passing football continued to curry favour with home supporters and despite more pressure and possession from Dundee, they didn’t overly alarm the Leeds rearguard.
One decent chance did arrive when the visitors, after a flurry of substitutions, saw replacements Mario Bilate and Charlie Telfer combine with the latter shooting off target when well placed.
United made a triple substitution on 62 minutes with Poleon, Chris Dawson and Lewis Cook coming on for Morison, Luke Murphy and Tonge respectively, with Morison handed a good ovation by supporters following a good shift, seven days on from being booed by a section of fans in the draw at Chesterfield.
One replacement, Dawson, robbed Connor Townsend and almost set up Poleon for a second before an error in the final ten minutes by former Dundee United player Noel Hunt almost led to a leveller, but Ryan Dow’s effort was turned away by Silvestri, his sole meaningful save of a largely quiet afternoon.
Leeds rubber-stamped the win on 86 minutes when an advantage was played by referee Andy Madeley following a challenge by Matt Smith on Fojat, much to the visiting fans’ dismay, with Poleon latching onto the loose ball and rounding Cierzniak before tucking the ball into the empty net.
Moments later, Poleon’s low shot was saved, with United able to reflect on a pretty positive afternoon following the final whistle.
Leeds United: Silvestri, Byram (C Taylor 74), Wootton, Pearce, Warnock (Berardi 46); Austin (Hunt 46), Bianchi, Murphy (Dawson 62), Tonge (Cook 62); Morison (Poleon 62), Doukara (M Smith 79). Substitutes not used: S Taylor.
Dundee United: Cierzniak; Dillon (Watson 51), Fojat, Morris, Townsend; Erskine (Spittal 54), Rankin (Dow 54), Patton (S Smith 68); Armstrong (Mackay-Steven 54); Graham (Bilate 54), Ciftci (Telfer 54). Substitutes not used: McCallum, Connolly, Fraser, Petrie.
Referee: Andy Madeley
Attendance: 10,115.