Bourneview Mill raced clear by 3-0 then had to survive Seagoe’s second-half fightback before securing full points.
Kyle Abraham’s acrobatic finish found the net to hand Bourneview control.
Smyth produced two teasing set-piece plays to help Bourneview increase the margin of victory.
Mark Boyce added the finishing touch on each occasion - the first a clinical header before a back-post finish.
Seagoe substitutes stepped off the sidelines after the interval and enjoyed an impact as Harry Proctor cut the deficit.
Jasir Silva left the tally at 3-2 but second-half pressure failed to result in an equaliser.
“Sam Nesbitt, Aaron Black, Harry, Chris Megaw and Kyle McMullan were all very good and we were better over the second half,” said Seagoe manager Matthew Wright. “We were disappointed to have conceded goals from corner-kicks during a poor first half.”
Bourneview boss Mark Jackson was happy to highlight the upturn in form.
“That’s now three wins on the bounce so everyone is feeling good,” he said. “I felt we controlled the game with the exception of maybe 20 minutes or so in the second half.
“The target now is to use this momentum to push on and it shows the squad depth that we got last weekend’s win despite missing six senior players.”
SEAGOE: Philip McCoy, Adam Breakey, Jason Greenaway, Alan Cantell, Geoff McCollum, Johnny Hanna, Robin Graham, Jasir Silva, Sam Nesbitt, Gareth Kerr, Aaron Black. Subs: Harry Proctor, Chris Megaw, Kyle McMullan.
BOURNEVIEW MILL: Andrew Neill, Steven Haugh, Thomas McClelland, Gavin Fox, Ross McDonald, Dale Compton, Geoff Neill, Simon Smyth, Kyle Abraham, Stephen Elliott, Mark Boyce. Subs: Tony Murray, Alan Haugh, Chris Woods.