The West Riding CA side struggled to adapt to the wet and windy conditions at Natty Lane but eventually got on top of their Halifax AFL rivals and had an abundance of possession.
Anthony McDonald opened the scoring midway through the first half from a short corner and 17-year-old Dennison doubled the advantage with a shot into the top corner.
Lee Smith and Simon Reekie caught the eye for Siddal, who got a goal back before the break.
Colin Matthews, McDonald and Declan Rothery combined superbly for the latter to make it 3-1 and Dennison's shot across the area into the bottom corner extended Irish's lead, Siddal replying with 10 minutes left.
Halifax Irish Centre had a 2-0 home win over Ossett Town Reserves to make it a great day for the club.
Their energetic, youthful side got the better of an Ossett outfit who wanted to stroke the ball around but were caught in possession.
Irish took the lead when the hard-working Dave Pearson broke into the box, was brought down and Chris Ellerby scored from the spot.
Paul Field and Michael Gregory did well for Irish who grabbed a second goal with 10 minutes left when the visiting keeper was caught in possession by Jake Griffiths.
Brighouse Town had an impressive 2-1 win at last season's beaten finalists Barnoldswick.
After a goalless first half, in which Glen Hall had the best chance for the visitors, Town went in front when Jamie Fradgley found Tom Holroyd, who fired home.
Barnoldswick levelled moments later through Mick Holt but Brighouse were not to be denied and substitute Christian Silkstone latched onto a Adam Hewlett through ball before finishing coolly.
Stump Cross had a fine 3-2 win away to former West Riding CA giants Crag Road United while Ryburn United had a stunning 5-1 home win over Thorne Colliery.
A Liam O'Neill 30 yarder after half an hour was the only score in the first period.
Craig Jennings unluckily scored an own goal, when he stuck out a foot at a corner, on 47 minutes but that proved a major spur to Ryburn who surged clear with an Owen Wilkinson free-kick, Paul Barker close-range effort, Adam Sharp shot from the edge of the area and a 20-yarder from Mark Butterfield.
Northowram threatened to create a shock when they led 2-0 at half time away to Harrogate Town Reserves' before going out 3-2.
The Rams had played well on last season's daunting trip to eventual beaten finalists Barnoldswick Town but stepped up on that effort at the well-appointed Wetherby Road ground.
Given the boost of a third minute goal from Matty Rushworth following a Chris Conroy corner, they doubled their lead after 23 minutes with an opportunist goal from last season's Division One player of the year James Hurtley, and were well worth their interval lead.
The shellshocked home side soon reduced the deficit after a defensive mistake but needed a somewhat suspect penalty decision to get on level terms. The Rams began to tire in the latter stages and fell behind 15 minutes from time but the Harrogate keeper was kept busy to the end and Conroy had a good chance to take the tie into extra time three minutes from the final whistle but his shot flew narrowly wide.
Another side to make a bold but unsuccessful bid were Luddenden Foot who went out 5-3 away to West Yorkshire League Premier side Leeds City after extra time.
The game started at a fast and furious pace with both defences holding tight.
Central midfielders Danny Kirman and James Dodd looked to have a slight edge over their counterparts and on 30 minutes the visitors took the lead when a fine through ball from Daren Smith caught out the advancing keeper for Alex Austin to nip in.
Foot allowed striker Chapman to stroll through and equalise straight from the kick off in the second half and Leeds began to play some attractive football.
They took the lead with Booth's fine individual goal but a fantastic late free kick from Kirman levelled it.
In extra time, Leeds killed the game with three quick goals before Gareth Gaukrodger's late consolation.