After a goalless first period, half-time substitute Levi Amantchi scored what proved to be the winner just six minutes after the break.
Jimmy McNulty made eight changes from the side that started last weekend’s abandoned game against Southend United.
Tom Myles started in goal, with a back three of David Tutonda, Liam Hogan and Dan Moss in front of him.
Ryan Galvin and Tarryn Allarakhia, two of the three to keep their starting place, were the wing-backs, with a midfield pairing of Casey Pettit and Jake Burger.
Connor McBride was the third of those who started against Southend to play here, alongside Liam Humbles and Ian Henderson. Humbles was a late addition to the line-up, replacing Aidan Barlow, who had initially been down to start.
On the bench, Tyler Smith returned from injury, with Bryce Hosannah and Liam Humbles also coming into the squad.
Dale created the first opportunities of the game, as McBride and Allarakhia both had efforts from inside the area blocked, whilst Henderson’s header from a corner was well saved by Eddie Brearey at his near post.
Galvin’s burst forward led to him firing a shot into the side netting, with Burger glancing a cross from Moss wide of the far upright.
At the other end, Myles was forced into some comfortable saves to deny Leamington efforts from range, whilst Seb Thompson curling a low shot inches wide of the goalkeeper’s right post.
Dale’s best chance fell to McBride shortly after the hour mark, when he was played in by Allarakhia. However, Brearey did well to turn his shot wide of the post.
In the last knockings of the first period, Ewan Williams nodded over a Leamington corner, whilst Hogan tried his luck from distance, firing into the arms of the home stopper.
At the break, Amantchi was introduced in place of Henderson, and within six minutes he had given Dale the lead.
A ball forward was played into his path, with the striker taking it under his spell and carrying it into the area, before moving it on to his right foot and curling one low into the far corner.
Humbles and Hogan both saw efforts fly narrowly off target as Dale looked for a second, although Myles had to be on hand at the other end to turn Miro Pais’ low shot wide for a corner.
Substitute Smith had a shot well blocked inside the area after neat work by fellow sub Anthony Gomez-Mancini, whilst Amantchi curled an effort wide of the far post after cutting inside from the right.
The hosts had a few efforts from range off target late on as Dale held on comfortably to progress to the next round.
Leamington XI | Brearey, Meredith, Quaynor, Tomlinson, Pais, Walker © (79’ Clarke), Williams, Thompson, Lynn (63’ Berridge), Crowther, van Lier (82’ Burton).
Unused subs | Humphries, Streete, Farmer.
Dale XI | Myles, Tutonda, Hogan, Allarakhia (62’ Hosannah), Pettit ©, Burger, McBride (62’ Smith), Moss, Humbles, Galvin (62’ Gomez-Mancini), Henderson (46’ Amantchi).
Unused subs | Broome, Ebanks-Landell.
Scorers | 51’ Amantchi.
Attendance | 421.
