With progression virtually assured Michael Laudrup had elected not to risk the fitness of captain Ashley Williams, record signing Wilfried Bony and midfielder Jonjo Shelvey with Sunday's Premier League trip to West Brom in mind.
From the off Swansea were uncharacteristically sloppy in possession, allowing their opponents to enjoy long spells in their half although they did not trouble Gerhard Tremmel.
Indeed, the German's main problem was the use of a laser pen by Petrolul's fans whenever the hosts had a set-piece near the Swansea goal.
Rory Donnelly was showing some nice touches but will feel he should have done better with two first-half chances.
The Northern Irishman dragged wide from Michu's delightful pass, and then could not beat Geraldo Alves as he bore down on goal.
But Petrolul should have led just before the interval. Ferebory Dore's header from a corner fell to Hamza, his shot was only half stopped by Tremmel and Britton had to head off the line.
Tremmel had more work to do early in the second half as he pushed a fierce drive from substitute Filipe Teixeira round the post.
As the hosts pressed further forward in search of the goals they desperately needed, they left space for Swansea to exploit and they were nearly punished when Donnelly raced clear, the striker tried to find Pablo Hernandez and Alves diverted the pass against his own post.
But, just as Swansea established some control, they conceded.
Priso got the better of Swansea's offside trap to stroll forward unopposed and beat the helpless Tremmel.
Lamah coolly finished from Alejandro Pozuelo's cross just moments later, but Hamza's header during a frenzied final few minutes gave the home side the win and Swansea's night ended on another low when Britton was giving his marching orders after kicking the ball away following a foul by Chico Flores.
|Petrolul Ploiesti||Team Statistics||Swansea City|
|0||1st Half Goals||0|
|5||Shots on Target||3|
|12||Shots off Target||3|
|58||1st Half Poss.||42|
|53.9||2nd Half Poss.||46.1|