The hosts threatened to start Rivals Weekend with a big shock, edging the first half with greater defensive intensity and exciting attacking sets.
It was a thrilling opening 40 minutes, not deserving of a rare pointless half.
However, Leeds opened the scoring right after the break, Momirovski reacting instinctively to dot down after a mistake in the Tigers defence.
The second was more orthodox, with the centre finding space on the right wing to storm home to the right of the posts.
Castleford’s intensity dropped after that second score, their guile and determination running out as Miller latched onto another defensive mistake to add a third try.
Simm’s score briefly threatened a late comeback, but Miller capped off a fine individual display by scoring his second try, after Croft had broken the line in centre field.
Leeds full-back Lachie Miller told BBC Radio 5 Live Sports Extra:
“It was a really tough night. In that first half they played the conditions really well and kept us in our corner. I think we had six or seven drop-outs in a row.
“But we had talked about starting games with intent and maintaining it, and in that first half our defence was outstanding. That is what won us the game.
“It’s a new spine, a new team and it’s not going to happen straightaway, we are well aware of that. But we have been working really hard and I think we can start hitting our stride when it matters.
“We have got a really good bunch of people and with the culture we are building, we love each other like brothers. That is going to stand us in good stead.”
Castleford: Broadbent, Simm, Hodson, Wood, Senior, Richardson, Miller, Lawler, McShane, Watts, El-Zakhem, Mellor, Westerman
Interchanges: Horne, Hall, Vete, Johnson
Leeds: Miller, Roberts, Newman, Momirovski, Handley, Croft, Frawley, Oledzki, Ackers, Sangare, Bentley, Martin, Smith
Interchanges: Lisone, O’Connor, McDonnell, Goudemand
Referee: Aaron Moore