Rangers goalkeeper Luke Herrick saved Morgan's attempt.
"At times we reasserted ourselves but it's a huge credit to Hastings Old Boys, who will upset a few teams."
Stephen Foulkes bagged a hattrick (12th, 48th, 68th), while Cory Janssen claimed the other two (82nd, 89th).
Ben Simmonds volleyed a screamer from 30m out in the 22nd minute to level terms before Morgan put the schoolboys ahead in the 46th minute.
Marist 4 Rovers 0
If the previous weekend was euphoric for the Napier City Rovers club, then this round was one to forget.
Hotshots Napier Marist thumped top-of-the-table Promotem Napier City Rovers 4-0 in the Park Island derby.
It mirrored the result of the Rovers' 4-1 loss to Western Suburbs in their Central League campaign in Wellington after a long weekend culminating in Chatham Cup celebrations.
Jack Needes scored twice and Jake Murphy and Dave Ellison once each, as Marist led 1-0 at halftime.
It was sweet revenge for the Green and Whites, who succumbed 2-0 to Rovers in the first round.
"From the kick-off we wanted it more and we got it," said Marist club captain Alan Dick, although he felt the match was pretty even in the first spell.
"In the second half we totally out-footballed Rovers," said a jubilant Dick, who was in the mood to buy a beer for anyone who walked into the clubrooms after the post-match prayers.
"Japan will never beat the All Blacks, so it wasn't a lucky win for us," he said.
Gisborne 2 Porth Hill 0
The only non-Bay team in the premiership, Sunshine Brewery Team Gisborne, will relish Rovers' loss as they tighten their grip on the top rung of the ladder with just one defeat.
Injecting two more schoolboys (Jarom Brouwer and George Andrew) yesterday at St Childer's Reserve, Gisborne beat AppMed House Port Hill United 2-0 after the sides were locked scoreless in the first 45 minutes.
Nicky Land found the net in the 61st minute, while Kieran Ryan kept his scoring habit with an 83rd-minute goal with Brouwer providing the platform.
"Port Hill played well and it was a great game to watch," Gisborne development officer Blake Mulrooney said, adding the balmy conditions were similar to those of the Bay.
Maycenvale 1 Taradale 5
Maycenvale United put up a good fight in the first half, trailing 2-1, but defending champions Your Solutions Taradale ground the Hastings club down in the second spell for a 5-1 win.
Nathaniel Wright scored twice, Dean Johnstone nailed a hand-ball penalty, and David Gearey and Jonathan Taylor got one each. Sam Ebbett scored for Vale.
"They tried to play football but in the second half we pulled away," Vale player/coach Chris McIvor said.
Federation League
Red Sox 1 Havelock 4
After a tough long weekend, including a heavy Chatham Cup loss, Cole Murray Group Havelock North Wanderers bounced back with a 4-1 victory in Palmerston North on Saturday.
The villagers beat Red Sox at Skoglund Park with Jared Bloor claiming two goals, BJ Christensen making good from the penalty spot and super sub Chase Keeney claiming one.
The 2m tall Keeny, here from Daytona, Florida, injured a thumb ligament as a goalkeeper but is making the most of his time on the field while recovering.
"We're pleased. It wasn't our best performance but we got the points," Havelock coach Bruce Barclay said.
Barclay said Fed League was stronger than the premiership so if his troops kept battling they would raise the bar.