Where the Scarlets came into the match in scintillating form, the Ospreys had endured a nightmare start to the campaign and lay second bottom of the RaboDirect PRO12.
However a Welsh derby was always going to bring the best out of the visitors and thanks to the efforts of second-half replacement Jones, who went over off the back of maul, and Dirksen, they finally got that first win under their belts.
George North's last-minute try did at least mean that the Scarlets went away with a losing bonus point - with Priestland holding his nerve for the final conversion.
The game was preceded by an impeccably-observed minute's silence for Nevin Spence who lost his life in a tragic farming accident last Saturday along with his father Noel and brother Graham.
And when the game did start the Ospreys could have taken the lead within the first 30 seconds when Dan Biggar went for an early drop goal only to slice his effort wide.
While Biggar also missed his first shot at goal, Priestland made no mistake slotting from in front of the posts after a high tackle by Joe Bearman to give Scarlets a 3-0 lead after just three minutes.
But Biggar drew the visitors level a couple of minutes later after Andy Fenby had been penalised at a breakdown.
Priestland missed a chance to put the Scarlets back in front but after Ospreys prop Aaron Jarvis was penalised, the Welsh international found his range from just inside his own half to make it 6-3.
In a fractious game the Ospreys responded when they got the better of a Scarlets scrum to earn another penalty - Biggar again on target to even things up.
The Scarlets should have been back in front when Ian Evans was penalised for a high tackle but Priestland was off-target with the kick.
The home side thought they were in front when Fenby went over in the corner but after consultation with the TMO it was ruled a knock on from the Scarlets winger under the attentions of Ospreys flanker George Stowers.
The Ospreys earned a penalty from the ensuing scrum and their set-piece was very much in the ascendancy. With five minutes remaining in the half they won another penalty, this time from a breakdown infringement and Biggar duly slotted it to put the visitors in front for the first time.
That was how it stayed until the break and Simon Easterby had clearly seen enough of his underperforming scrum and hauled off Deacon Manu, replacing him with Samson Lee for the second half.
But it was the visitors who started the second half quicker, and thought they had scored the first try of the match only for Dirksen to be called back for a forward pass.
And despite the visitors appearing to have the momentum a penalty given away by Duncan Jones allowed Priestland to slot another penalty and make it 9-9.
The Scarlets scrum looked much stronger with the introduction of Lee and they earned a penalty just before the hour mark but Priestland's attempt just went wide.
However just as it looked as though the Scarlets had resolved their scrummaging issues, they conceded another penalty and referee Leighton Hodges sent Lee to the sin bin.
Rather than capitalise the Ospreys allowed the Scarlets to take the initiative and Priestland had another chance to put his side in front only to hit the post from wide on the left.
Lee returned as the Scarlets completed their ten minutes at 14 men without conceding but almost immediately after Jones capitalised on some poor fringe defence to score.
And with the Scarlets forced to take chances the visitors got themselves into a good position once more and the ball was spread wide for Dirksen to score his second try of the season - Biggar slotting both conversions from wide on the left.
With the Scarlets pushing for a losing bonus point Jonathan Thomas was sent to the sin bin and the home side took full advantage as North dabbed down despite being out of play himself and Priestland did the rest.
|Scarlets Score Card|
|Ospreys Score Card|