Aaron Harmon hopes this win can be a turning point in Glentoran’s season of woe.
Jonny Smith scored an 89th minute penalty to record the Glens’ first league victory in almost two months.
“This result is going to breed confidence throughout the whole squad,” said Harmon.
“We can build on this now and hopefully go into next week, produce another good performance and move up the table.”
A tight match produced few clear-cut chances, although both sides did hit the woodwork.
Chris Hegarty struck the crossbar for the home team after getting his head to a corner from Jamie Glackin.
The Glens’ James Ferrin then saw his header bounce off the woodwork.
Dungannon keeper Andy Coleman was also to thank for keeping his side level when he completed a double save from Jay Magee and Ciaran Caldwell.
However, Smith broke through, was fouled by the keeper and tucked away the spot-kick to deliver Gary Haveron’s first win as Glentoran boss.
“We set out to be very solid and hard to beat today,” added Harmon.
“We knew we would get a couple of chances, and thankfully at the end the penalty came.”
For Dungannon this was a disappointing conclusion to a week which had brought six-goal wins over Portadown and Ballinamallard.
“The first 10 minutes was the only positivity I can take,” said Head Coach Rodney McAree. “I don’t think we did enough over the rest of the match.”
McAree admitted Dungannon need to perform at a high level more regularly if they are to achieve their ambition of a top six finish.
“Our consistency levels have to remain the same if we have any ambition of going on to achieve something,” he added.