It was an unconvincing first half, though, with the visitors breaking the Rovers' brittle defence at will, mostly on the right flank.
Marist striker Jordan Martens duffed in the third minute with a gaping goalmouth before going on to sky the first penalty kick in the shootout phase.
"We were poor in the first half but we started dominating in the second half before the red card," Robertson said.
"We went 3-1 up and were in control but the red card changed the game. To their credit they showed character to get back into the game."
The hosts will analyse video-tape footage to tweak their defensive flaws.
Wearing a wry smile, Palmy coach Simon Lees said the teams were habitually making fans reach for heart pills.
"In the first half we had three to four chances where we didn't quite put it in the back of the net.
"Napier are a good enough team to make you pay for it," Lees said, adding Marist were the only team looking for a victory.
Martens, who looked inconsolable, "would be all right because he's a good player".
In the 17th minute, striker Jerram Tuck latched on to a through ball from centre-mid Michael Crisford to push the ball past an advancing goalkeeper Jonty Underhill. The ball clipped the left upright before going in for a 1-0 lead.
Martens again shot wide with just Underhill to beat in the 35th minute. Two minutes later, he ignored Crisford's plea inside the 18m box to lay back and instead shot wide.
In the 40th minute, Welsh import Miles John took two players on to cross from the right flank of the goal line to Angus Kilkolly who caressed the ball wide of the left upright from a gimme range.
In the 53rd minute, Palmy defenders conceded a penalty for holding Chris Greatholder in the 18m box.
English import midfielder Ryan Tinsley had Singh moving to the wrong side to level, 1-1.
In the 58th minute, Palmy's Michael McKnight tripped Andy Bevin in the box. Bay referee Gareth Sheehan pointed to the penalty spot.
Singh called Tinsley's bluff as the midfielder went for the keeper's left without joy but a diligent John followed up like a terrier to blast it into the goal for a 2-1 lead although Marist argued the Welshman had run into the box before the keeper parried.
Ref Sheehan consulted the teenage assistant Brad Brunton before awarding the goal.
In the 70th minute, Underhill kept Rovers ahead when he denied Tuck. Four minutes on the Rovers shot ahead 3-1 after John adroitly wrong-footed two defenders from a thwarted freekick to curl it to Bevin on the far post. The midfielder drilled it in.
In the 79th minute, Tinsley tripped an attacker on the edge of the box to have an early shower for his second yellow card.
Five minutes later Palmy substitute Rhys Galer tapped in a cross from the right flank from point-blank range, 3-2.
Two minutes into added time, substitute Fin Milne, jostling in the free-kick wall, rose to nod the ball past Underhill for another cup extra time in consecutive rounds after Rovers beat Wellington Olympic 5-4.
This time it went to penalty kicks.
Matt Hastings, Bevin, John, Messam and Josh Stevenson turned in a perfect report card.
Fin Milne, Jeremy Wild, Dom Milne and Tuck kept Palmy's hopes alive.
Unlike last year, the visitors had no fairytale ending. Park Island remains a fortress this season for Danny Wilson's undefeated troops.
It was salt in the wound for Marist when Crisford picked a red card for mouthing off to the ref while waiting for the penalty kicks.
