Crawley took the lead in the third minute through Collins, but Newport County drew level on 33 minutes through Joss Labardie.
However two goals in the second half by Yorwerth and Smith earned Crawley a 3-1 win.
Dermot Drummy named an unchanged side from last Saturday’s which won 2-0 away at Crewe Alexandra.
Defender Joe McNerney returned to the squad after seven weeks out following an operation to his knee.
He was named on the bench.
Reds made the perfect start to the match by taking the lead in only the third minute when Lewis Young crossed to Collins who headed in from close-range.
Newport had a couple of long-range efforts by Tom Owen-Evans which flew over the bar and wide.
A tussle in the area saw Jordan Roberts for Crawley and Josh O’Hanlon for Newport both pick up yellow cards.
The game became heated and there was controversy when Roberts received a two-footed challenge from captain Scot Bennett, and Enzio Boldewijn and Josh Payne were booked, as well as Bennett himself.
Newport then equalised on 33 minutes when Labadie’s shot took a deflection by Yorwerth on its way into the net.
County made an substitution when Rhys Healey came off the bench to replace Marlon Jackson.
Reeds were fastest out of the blocks at the start of the second half when they scored twice in six minutes.
Yorwerth made amends for accidentally helping in the Exiles’ equaliser when he scored in the 48th minute.
He nodded in Smith’s cross from a free-kick.
Smith then made it 3-1 three minutes later, putting away low from the edge of the area from Roberts’ cross which headed down to him by Collins.
Roberts missed the perfect opportunity to seal the three points with 15 minutes to go when Roberts missed an opean goal from short-range.
Goalkeeper Glenn Morris kept Reds’ two-goal lead with a full-length save to tip over an on-target free-kick by Josh Sheehan.
In added-time Newport were awarded a late penatly following a foul on Healey who stood up to take the spot-kick.
Healey which he put in after it rebounded off the crossbar.
However the goal was disallowed by the referee as it was technically a dead ball after hitting the crossbar and another player needed to touch it in between his two shots.
REDS: Morris, Young, Payne, Connolly, Boldewijn (Bawling 80), Smith (capt), Roberts (Yussuf 86), Blackman, Yorwerth, Clifford (Djalo 90), Collins.
Unused subs; Beeney, Davey, McNerney, Henderson
NEWPORT: Day, Bobb, Jones, Labadie (Green 65), Myrie-Williams, Tozer (Wood 75), Jackson (Healey 46), Sheehan, Bennett (capt), Owen-Evans, O’Hanlon
Unused subs: Randall, Bognot, Bittner, Meite
REFEREE: Nick Kinseley
ATTENDANCE: 2,022 (168 away)
MAN OF THE MATCH: Josh Yorwerth
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