Yeltz manager Paul Smith was delighted with the result and the performance.
"It was a brilliant hat-trick from Chris Lait. We created lots of chances in spells and could've scored more - but the clean sheet was also important to us today. The games are coming thick and fast now but momentum is building and we're looking forward to the draw for the next round."
Halesowen dominated the first half on a wet surface and took the lead after just six minutes when Ahmed Ali outmuscled the Sutton midfield to supply Lait and he held off the last defender to slot past goalkeeper Lewis Gwilliams from 12 yards.
With the Yeltz in control, visiting goalkeeper Gwilliams parried away from Jack Holmes at the end of a mazy run and a clever back flick from Kyle Finn fell agonisingly wide after full-back Brett Lloyd overlapped down the left to cross after half an hour. Finn's 31st minute free-kick then found captain Paul McCone at the far post but his low header was turned over the bar by Gwilliams.
Lait made it 2-0 in the 40th minute when he met Finn's great forward pass and side-stepped his marker to curl home.
The Royals had to wait until the 45th minute for their first decent chance when Jack Burgess lofted the ball over the bar and Sutton then made a better start to the second half by winning a couple of corners.
But the Yeltz moved into a higher gear once again and Lait smashed home to complete his hat-trick in the 64th minute after Sutton failed to clear Lewis Wright's low dangerous cross from the right. Substitute Jamie Molyneux put the ball just wide at the end of a lovely move three minutes later after substitute McKauley Manning set up Wright to cross again. James Beresford planted a good header over the bar for the well-beaten Royals from a 79th minute corner but the hosts never looked in any real danger.
Late on, Halesowen's Manning struck an 85th minute free-kick into the arms of Gwilliams and Gwilliams collected a glancing header from substitute Joe Palmer. Gwilliams then saved with his legs from Molyneux after 89 minutes and opposite number Platt gathered from Sutton substitute Rikardo Reid in the dying seconds.
Halesowen Town: Dan Platt; Lewis Wright, Brett Lloyd, Ahmed Ali, Paul McCone (c), Rob Evans, Jack Holmes, Toby Scott (McKauley Manning 50), Harry White (Jamie Molyneux 46), Kyle Finn, Chris Lait (Joe Palmer 78). Subs Not Used: Calum Flanagan, Jac Redhead.
Sutton Coldfield Town: Lewis Gwilliams; Aris Christophorou (c), Harry Eden, Sufyan Zia (Joel Powney 46), James Beresford, Emem Jones, Rhys Hilton (Jordan Francis 46), Ryan Shaw (Rikardo Reid 65), Reece Gibson, Desgan Martin, Jack Burgess. Subs Not Used: John Dodd, Vinnie Dwyer, Kieran Hart, Dalmar Morrison.
Referee: David Hinton