Byrne scored twice and provided yet another assist for the other goal to deservedly see the Gladiators home against a talented Marske outfit who battled to the bitter end.
Matlock dominated for seventy per cent of the tie and maybe in that spell should have put the match well and truly to bed. But a scrappy last quarter of an hour or so and game management that could have been better from the Gladiators saw the visitors come back from a 3-1 deficit to set up a nervy finale.
Matlock began well and Ross Hannah was through on goal inside the opening 20 seconds only for Kev Burgess to produce a magnificent sliding tackle as Hannah was about to pull the trigger.
In the third minute Alex Wiles then broke through and pulled his shot wide with only goalkeeper Liam Watson to beat.
In their first attack the Seasiders rocked their hosts with the opening goal. Matlock failed to clear their lines effectively and Adam Boyes, with 32 goals under his belt this season, crossed from the right for an unattended Matty Tymon to net with a firm close range header with seven minutes on the clock.
But Matlock responded positively and swiftly. Byrne whipped in a teasing low corner kick which flashed low into the opposite corner for a tenth minute leveller.
Within a further three minutes Matlock had turned the game on its head as Liam Hughes fed Byrne on the right who delivered an inch perfect high cross for Reece Kendall to head home.
Dale Hopson drove too high for Marske after a free kick had only been partially cleared and a shot from Curtis Round was well blocked by Ryan Qualter.
Hughes again supplied Byrne who lifted his shot narrowly too high before Marske keeper Watson had to be replaced after suffering an injury, Ryan Catterick taking his place.
Hughes headed just too high for Matlock before the break and immediately after the resumption Boyes and Tymon went close for the visitors.
But Matlock surged two goals in front with another memorable strike from Byrne who after equally delightful build up play from Hughes and Hannah, curled a wonderful shot in off the far post from 16 yards.
Suddenly the zip returned to the Gladiators’ play, Byrne’s 30-yarder dropped wide before a scrappy last 20 minutes saw Matlock concede but ultimately do enough to qualify for the next stage.
Tymon halved the deficit, heading in a Craig Gott free kick with four minutes to go.
They sensed salvation and a possible penalty shoot-out and Tymon touched a cross narrowly wide but Marske would not go as close again.
Catterick was up for a late set piece and went in late on Paul Cooper to cause a melee to increase Marske’s frustration but Matlock had done enough in a thoroughly entertaining game and will now look to create an upset against York in round three.