Portadown enjoyed a positive start as Sam Simpson curled a shot over the bar following neat passing by the visitors.
Smyth proved sharp on his 19th birthday and caused problems on 15 minutes by picking up Jamie Mulgrew’s pass and whipping in a dangerous cross which Ports captain Keith O’Hara had to cut out on the run.
Ross Gaynor’s corner-kick was then met by a looping Mark Stafford header which David Miskelly managed to punch clear under pressure.
Linfield grabbed the upper hand before the half-hour mark thanks to Gaynor’s slick strike beyond Miskelly after Mulgrew’s pass was chested down on the edge of the box by Andy Waterworth.
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Simpson had another sight of goal soon after when Linfield failed to clear a Mark Carson free-kick - but the winger’s low drive dropped the wrong side of the post.
Portadown closed out the half with Alan Byrne meeting Brendan Shannon’s corner-kick but the recent signing struggled to keep his header under the crossbar.
Linfield doubled the lead within the opening moments of the second half.
A Smyth corner-kick from the left was met on the run by Stafford and O’Hara blocked the downward header on the line. The match officials, however, awarded a goal despite Ports protests that the ball did not cross the line.
Teenage striker Nathaniel Ferris led the line for the Ports and blasted an angled drive goalwards as the away side attempted to get back into contention.
Roy Carroll was forced into his first save of the afternoon on 66 minutes as he pushed wide a long-range drive by Niall Henderson.
Linfield increased the lead to 3-0 on 72 minutes, with Smyth popping up inside the penalty area to tuck away a close-range shot.
Two Linfield substitutes combined to carve out another opening when Kirk Millar’s cross was met on the volley by Kris Bright but Miskelly dropped low to save.
The Ports gained a consolation for some positive passing when Robert Garrett smashed home an angled shot from distance into the top corner.
However, the match ended with Linfield celebrating a fourth goal thanks to a defensive mess by Portadown. Attempts to pass it out from defence resulted in a loose ball which Millar returned into the box for substitute Aaron Burns to head home.
LINFIELD: Carroll, Stafford, Clingan, Callacher, Waterworth, Clarke, Casement, Fallon, Mulgrew, Gaynor, Smyth. Subs: Bright (Fallon, 68), Millar (Smyth, 77), Burns (Mulgrew, 77), Ward, Quinn.
PORTADOWN: Miskelly, Carson, Rodgers, Byrne, O’Hara, Garrett, Henderson, Hughes, Ferris, Shannon, Simpson. Subs: McGaughey, McAllister (Ferris, 71), Mouncey (Shannon, 88), Kirwan (Hughes, 71), Withers.
Referee: Raymond Hetherington.