Conlon fired home on nine minutes and Gritton grabbed his goal in injury time after Gareth Sheldon had given Hereford hope following Michael Boulding's second goal for the Stags.
After a scrappy opening, it was Mansfield who gained the early advantage and it was one of their two midweek signings who made the breakthrough.
Conlon, who along with loan-signing Gritton, joined the Stags in midweek, pounced to rifle home a shot after the Hereford defence had made a mess of trying to clear Stephen Dawson's cross.
The Bulls tried to strike back with Alan Connell firing in a long-range effort who easily cleared the bar.
United then forced three corners in quick succession but Andy Ferrell's corners were comfortably dealt with by the visitors' defence.
It was Mansfield who came closest to extending their lead on 20 minutes when Giles Coke raced past Luke Webb and into the Hereford area. But Wayne Brown was equal to the midfielder's shot, diving to parry away brilliantly.
Ten minutes later, a deep free-kick by Matt Hamshaw found John Mullins steaming in at the back post but the full-back blazed his effort high over the bar.
Mansfield keeper Jason White pulled off a good save when Ferrell's free-kick found its way through early in the second period, but Hereford generally found it difficult to make much impact.
And, as they chased the game the Bulls were hit on the counter-attack when Dawson's pass sent Coke away on the left to pull the ball back for Boulding to ram home the second on 78 minutes.
Hereford threw everything into attack in a bid to salvage something from the game and a neat move involving Tim Sills and Andy Williams led to substitute Sheldon firing in off a post.
But if the Bulls thought that might bring a late come-back they were to be disappointed when Hamshaw raced away on the right and crossed for Gritton to mark his debut with a goal of his own.