The result was a disappointing outcome after a positive opening forty minutes where they had looked the side most likely to come away with the points.
Defeat also saw Vale leapfrog Town in the standings and was the third defeat in four games for Simon Weaver's side, a run that has also seen them fail to find the net.
There were two changes from the side that drew 0-0 away at Walsall on Good Friday, with Lloyd Kerry and Josh McPake both coming into the starting line-up in place of Ryan Fallowfield and Aaron Martin.
The visitors named an unchanged side from the one that beat Exeter 1-0, their fourth win on the bounce.
The game had a note of history to it with Rebecca Welch becoming the first female referee to officiate at an EFL game.
Town registered the first effort on goal of the game when a direct Josh McPake run resulted in his shot being blocked to safety.
On 17 minutes Mark Beck found himself unmarked from a George Thomson free-kick but although he managed to hit the target Scott Brown comfortably dealt with the danger.
McPake was causing Vale plenty of threat in the opening stages and his run behind the defence again forced Brown into action with the visitors keeper also denying Jack Muldoon's follow-up effort.
An obvious danger to the Town defence was the pace of Devante Rodney and when he got the better of Warren Burrell James Belshaw had to be at his best to keep the scores level.
Despite the positive opening forty-five minutes Town were immediately behind after the break. From a long throw Worrall found himself in plenty of space and crashed home a volley beyond the helpless Belshaw.
Thomson then went into the book soon after pulling back Worrall when he was advancing into another threatening position.
Having got their noses in front Vale looked to consolidate their position by making a double change on the hour with Guthrie and Jake Taylor replacing Devante Rodney and Emmanuel Oyeleke.
With Town struggling to make inroads into the Vale defence in the second half Simon Weaver threw on Aaron Martin in place of Thomson.
And Martin was in the thick of the action soon after when he met a teasing cross from Dan Jones but he failed to direct his header on target.
Substitute Guthrie then tested Belshaw from distance in what was a a rare attacking moment as with both sides largely failing to apply any pressure on the opposition defence.
With 10 minutes remaining Brendan Kiernan replaced Muldoon but aside from a near post clearance from a Martin cross Town failed to worry the Vale defence and Guthrie sealed the win in injury time when he fired beyond Belsahw.
Town: Belshaw, Burrell, Jones, Smith, Hall, Thomson (Martin, 67), Falkingham, Kerry, McPake, Beck, Muldoon (Kiernan, 80)
Subs not used: Minter, Martin, Francis, Williams.
Booked: Thomson (51)
Port Vale: Brown, Joyce, Legge, Smith, Worrall, Oyeleke (Talyor, 62). Conlon, Montano (Olagunju, 90), Robinson (Cullen, 87), Brisley, Rodney (Guthrie, 62).
Subs not used: Amoo, Hurst, Scott.
Goals: Conlon (47), Guthrie (90)
Booked: Conlon (60)
Referee: Rebecca Welch.