Job done for Stuart Gray and the Clarets as they eased into the fourth round of the FA Cup with a comfortable victory over the League Two side.
In the final game of his initial three-match spell in charge, Gray made sure Burnley's next permanent manager will have a last-32 tie to look forward to at the end of the month as he masterminded his second win in eight days at Turf Moor.
Even though Vale quickly cancelled out Clarke Carlisle's early goal to sniff a possible giant-killing, the Clarets were never really in danger once Tyrone Mears had restored the lead before half-time.
Vale were far from pushovers in their first game under new boss Jim Gannon but the two-division gap was best illustrated by the class of Mears and Chris Eagles and Eagles' stunning goal early in the second half virtually guaranteed Burnley's passage through.
Graham Alexander made sure with a late penalty as Vale refused to lie down thanks to two goals from the eye-catching Robert Taylor.
Clarke Carlisle heads Burnley in front
And having achieved what they had to do, the Clarets made sure Gray ended his temporary spell on a high if there is to be a new man in the dug-out for next Saturday's more demanding test against Championship leaders Queens Park Rangers.
Having declared his intent by naming a strong side - which included Danny Fox at left-back following a two-month injury absence - Gray could not have enjoyed a better start.
There were only four minutes gone when the Clarets went ahead through Carlisle.
The defender had stayed up following a corner and when Eagles delivered a perfect cross to the far post Carlisle made no mistake in heading home his third goal of the season from no more than six yards out.
In dealing such an early blow Burnley might have expected a straight-forward afternoon but to Vale's credit the underdogs responded in positive fashion and levelled after quarter of an hour.
The Clarets' inability to keep a clean sheet has hampered their Championship form and they were again guilty of defensive uncertainty as Taylor helped himself to the equaliser.
Initially opened up by Justin Richards down the inside left channel, Louis Dodds thought he had scored when he turned Richards' low cross goalwards.
Tyrone Mears curls in the Clarets' second
Michael Duff cleared the ball off the line but Duff and Carlisle - perhaps expecting the goal to be given - then hesitated over completing the clearance and Taylor pounced to drive home the loose ball.
However, the prospect of a shock lingered for no more than five minutes before the Clarets regained the advantage.
Vale never got to grips with Eagles all afternoon and after a typically penetrative run had been ended by Anthony Griffith's trip 25 yards from goal, Mears stepped up to curl the resulting free-kick into the bottom corner.
Having been given a scare the Clarets looked to make sure there would be no repeat as they then went in search of a third goal before the break.
Chris Iwelumo headed just wide from another Eagles cross before failing to connect cleanly with a shot on the turn after Eagles and side-kick Mears had again teased opened the Vale back line.
It's 3-1 thanks to Chris Eagles
Eagles was a constant threat to the League Two side and after Iwelumo returned the compliment he had a chance to score himself but for once lacked the composure to hit the target from just outside the penalty area as Burnley went in with a 2-1 lead.
That lasted just five minutes into the second half, though, as Eagles got the goal he deserved as the Clarets killed off the tie in style with a fantastic break-away effort.
From defending a corner one moment, the Clarets had the ball in the Vale net within seconds thanks initially to Wade Elliott.
Carrying the ball away from goal, Elliott released Jack Cork with a superb pass which Cork met on the run to go past Griffth before rolling the ball square to Eagles who unerringly side-footed his eighth goal of the season into the top corner.
Jay Rodriguez then forced Stuart Tomlinson into a scrambling save with a fiercely struck long-range effort but Vale weren't quite done and Gary Roberts was close to pulling one back after 65 minutes when he worked a nice one-two with Richards but lifted his shot onto the roof of the net.
And game over courtesy of Graham Alexander's spot-kick
It then took a timely interception from substitute Andre Bikey to deny Lewis Haldane after the impressive Taylor had worked another opening for the visitors, who refused to go down without a fight.
And Taylor himself almost added his second before Lee Grant rushed off his line to make a smothering save and spare the Clarets a potentially nervy finish.
That possibility was then snuffed out for good with 15 minutes to go thanks to Alexander's penalty.
Again the deadly duo of Eagles and Mears prised open the visitors' defence and when the out-paced Collins pushed Mears to the ground, Alexander stroked home his fourth successful spot-kick of the campaign.
For the second week running the Clarets had hit four on their own turf but Vale left with plenty of credit, enhanced further by Taylor's second goal in the 83rd-minute as he had the final word with a smart finish after Grant could only parry a piledriver from substitute Sean Rigg.
Burnley: Grant, Mears, Fox, Duff (Bikey 60), Carlisle, Alexander, Cork, Elliott (Marney 72), Iwelumo (Thompson 72), Rodriguez, Eagles. Subs: Edgar, Wallace, Easton, Jensen.
Port Vale: Tomlinson, Yates, McCombe, Owen, Collins, R Taylor, Griffith, Dodds (Morsy ht), J Richards (Fraser 77), Haldane (Rigg 77), Roberts. Subs: K Taylor, Bell, Sutton, Martin.
Booked: McCombe 35, Morsy 87.
Referee: Eddie Ilderton