Duku’s goal came in a pulsating first-half in which Town went toe-to-toe with the promotion-hopefuls, and came out on top. The half ended with Solihull’s Lee Vaughan being sent-off.
The second-half wasn’t as rip-roaring, but just as satisfying for Town, as they defended solidly before Rodney sealed the victory.
A cursory glance at the table, never mind the accompanying statistics, told Town the scale of the task in-front of them against The Moors, but Solihull were made to look like a team mired in mid-table obscurity, not going for the title.
Any Premier league or Championship season-ticket holders at The Shay will have considered a tenner very good value for money. They should come more often.
Josh Staunton made his first league start since being sent-off in the 1-1 draw at Dagenham on December 8, while Duku came back in alongside Rodney, and both excelled.
Town’s proud defensive home record came under serious threat early on as Sam Johnson was forced into a fingertip save from George Carline’s header across goal.
Moments afterwards, Alex Gudger spurned a glorious chance when he sent a free header wide from five yards in-front of goal.
It could have been 2-2 in the first 10 minutes through, with Devante Rodney’s free-kick whistling narrowly wide before James Berrett’s close-range shot was blocked by Vaughan after a burst foward by Rodney.
Solihull skipper Kyle Storer then got into the spirit with a wonderfully-inventive effort as he tried to chip Johnson - no mean feat - with a free-kick near the halfway line, and his attempt clipped the bar on its way narrowly over.
Kosylo prodded just wide after a characteristic burst forward in the inside-left channel as Town attacked with purpose and penetration.
Berrett then produced an outstanding through ball that sent Duku clean through on goal, and the absent Solihull defence could only watch as the striker coolly picked his spot and side-footed past Ryan Boot at his near post.
The ball broke to Duku again moments later to the left of the box, but hesitancy meant he was soon closed down, and the sight of goal disappeared.
Kosylo exemplified the confidence flowing through The Shaymen by flicking the ball over Vaughan, but then fired off target.
Solihull still offered a threat - Darren Carter curled a shot wide, Nathan Blisseet volleyed over off-balance, and Carline’s shot was bravely blocked by Matty Brown - but Town were sharper and quicker.
A lovely one-two between the front-two sent Rodney away before he was crowded out, but the move was kept alive, and Duku ended up shooting wide of the near post.
Duku and Rodney were always ready and willing to run onto through balls, and had the pace to do so.
Solihull had found them too hot to handle, struggling to live with their movement, work-rate and energy.
The visitors hadn’t really got into their stride - coming up against the typically brave and commanding Nathan Clarke and Matty Brown - whereas Town were at full pelt, led from the front by the impressive Duku and Rodney.
Moors’ task was then made even harder when Vaughan was then dismissed for a high tackle on Kosylo near the halfway line in first-half stoppage time.
Town were like a coiled spring after the restart, not letting Solihull drag them out of position, staying solid, and then pouncing on the break when the chance arose.
It was less end-to-end, 100mph stuff in the second-half, with Solihull enjoying more possession than may be expected for a side with 10-men, but finding - as many sides have at The Shay - that chances are hard to come by for visiting sides. It’s now eight hours since the last one.
Duku and Rodney combined well again on the hour-mark when the former’s clever header was latched onto by the latter, but he fired over from just inside the box under pressure from a defender.
The Shaymen broke again with real malice as the ball was nicked away from Solihull near the halfway line, and after charging forward, Duku’s pass over to Kosylo was then squared to Berrett, but Boot tipped away the low shot.
Solihull pressed for an equaliser, never creating a golden opportunity but exerting enough pressure to make it uncomfortable viewing for the Halifax fans.
Town’s earlier composure going forward had deserted them somewhat, with their strenuous efforts also perhaps catching up with them.
But the points were wrapped up when Rodney’s tenacity won the ball against the last Solihull defender, and he kept his cool to slide the ball under Boot.
Halifax: Johnson, Duckworth, Clarke, Brown, Skarz, Staunton, Berrett (King 77), Maher, Kosylo (Gondoh 86), Rodney, Duku (Quigley 67). Subs not used: Rowley, Preston.
Scorers: Duku (14) , Rodney (81)
Shots on target: 4
Shots off target: 10
Solihull: Boot, Vaughan, Daly, Gudger, Reckford (Yussuff 81), Carter, Storer, Hawkridge (Williams 84), Carline, Wright (Hylton 59), Blissett. Subs not used: Stenson, Maxwell.
Shots on target: 3
Shots off target: 13
Referee: Sam Purkiss
Town man of the match: Devante Rodney