Sampdoria were level eight minutes later as Gianni Munari climbed highest to head in from close range after a precise delivery from Eder.
Palermo continued to press forward after the break and reclaimed the lead in some style through Josip Ilicic. The Slovenian slalomed through three defenders before sending a composed low finish into the far corner.
Skipper Miccoli was then instrumental again with an assist as Sampdoria fell further behind on the hour mark.
His cross found the run of Santiago Garcia and the winger made no mistake to put the visitors 3-1 ahead.
Palermo held firm in the closing stages to secure three points that give them fresh hope of escaping relegation.