Johnstone opened the scoring with a close-range tap-in on eight minutes.
The 21-year-old slotted Bobby Barr's cross into the bottom corner for his 14th goal of the season to make it 2-0, before Paul McMullan added a third.
Dale Hilson and Gary Oliver hit back for the visitors but Morton held on for the win.

The SSE Swalec Stadium was the venue for an Ashes Test and a double-header of men's and women's T20 games.
The club turned in an operating profit of £593,000 after losing £87,000 in 2014.
But the accounts also show a fall in income from domestic cricket.
Chief executive Hugh Morris highlighted the success of staging international cricket in his report to members for the annual general meeting taking place on 31 March.
"Our priority was to deliver sell-out crowds and we were delighted to fill the ground not only for four consecutive days of Ashes cricket, but also for the T20 international," he wrote.
"We were particularly proud to receive our highest ever customer experience rating for the Ashes Test."
The match was the third Test in Cardiff, which will host England one-day matches against Sri Lanka and Pakistan in 2016, with international games scheduled until 2019.
2015 saw Glamorgan finish fourth in division two of the Championship and narrowly miss out on a place in the T20 Blast quarter-finals.
Morris warns the club must improve its income from county cricket and from the use of the stadium, admitting that membership numbers and money taken on the gate from spectators are on the decline.
"The current squad size and the development of our own cricketers are only going to be improved by increases in our own income," he wrote.
"It is vital we improve our core product, increase gate numbers, revitalise memberships, attract sponsors, consolidate our conferencing business, and development other sources of income."
Pop group Simply Red will headline the first major music concert at the stadium in July with another concert to be announced shortly.
But the financial year was also notable for the club having to ask for major debts to be written off.
Cardiff Council agreed for £4.4m of debt to be cancelled, while Allied Irish Bank also agreed a 70% write-off of its debt and former chairman Paul Russell accepted a 75% loss.
Morris's report thanked departing coach Toby Radford and groundsman Keith Exton for their work, while urging members to get behind new head coach Robert Croft and captain Jacques Rudolph.

Last month a report found South Ribble Council had a lack of awareness about ensuring passenger safety issues surrounding taxi licence applications.
Tory councillor Margaret Smith had faced calls for her to quit from her own party over the handling of the taxi licensing row.
A full council meeting was informed she resigned due to "ill health".
Ms Smith, who has been leader of the authority for the past nine years, was not present at the meeting in Leyland.
Her resignation letter was read out by chief executive Mike Nuttall and was "with immediate effect".
An audit of taxi driver licence applications in December had found appropriate background checks had not been carried out in relation to 40 working taxi drivers in South Ribble.
An independent report, written by solicitors Wilkin Chapman LLP in June, concluded the issues surrounding taxi licence applications had been addressed so it was not necessary to make any further recommendations.
Earlier this week, four of Ms Smith's Conservative colleagues resigned from the group, saying they could not support the leadership due to "ongoing circumstances and failures".
The council is now under no overall control for the first time in almost a decade.
Councillor Colin Clark was unanimously voted in as the interim leader of the authority at the meeting on Wednesday.
Councillor Cliff Hughes, who has worked with Ms Smith for over 30 years, said she was "hard working and a "good colleague" who "gets on with the whole group".
He said one of the "great strengths" of the council was that "whilst the parties are diverse, we do actually get on together and make decisions together and I think that's because Margaret led us into that".
Denny Johnstone netted a first-half brace as Morton returned to winning ways with victory over Queen of the South.
[NEXT_CONCEPT]
Hosting England versus Australia matches helped Glamorgan to record a profit for 2015, thanks to a surplus of £1.36 million, according to the club's annual financial report.
[NEXT_CONCEPT]
The leader of a council at the centre of claims children were sexually exploited by taxi drivers has resigned.