The Brazilian struck either side of the break, before a third goal by David Di Michele sent the Serie A side cruising into the group stage with a resounding four-goal aggregate victory.
Only five minutes were on the clock when the tormenting Carlos Tevez cut in from the left flank before letting fly with an angled 12-yarder that was tipped over by Alberto Fontana, before Carlton Cole headed wide and Paul Konchesky had a go from 20 yards.
With scarlet, smoking flares blazing on the home terraces of the Curva Nord, Simplicio tested the alert Roy Carroll with a low 20-yarder and then the Hammers keeper was forced into an exceptionally brave double save after Di Michele stole in between the hesitant Konchesky and Danny Gabbidon.
After seeing Greek referee Georgios Kasnaferis caution Andrea Barzagli for scything through him, the energetic Cole then scuffed across goal, before Konchesky sent another 20-yarder whistling past Fontana's left-hand post.
The theatrical Palermo keeper then palmed Marlon Harewood's acrobatic overhead kick skywards and, with the Hammers getting on top, Cole's shot thudded back off Fontana, who was then forced to tip over James Collins' goalbound header.
As the half-hour mark passed, the pink-topped Sicilians were wobbling but the Hammers were, equally, destined to pay for not finding the net.
For on 34 minutes, that man Simplicio climaxed a short free-kick with a low 18-yarder that flew back through a forest of legs and beyond the sprawling Carroll, to double Palermo's aggregate advantage.
West Ham had kicked off needing two goals for outright victory and they started the second half in an identical position too.
Carroll was soon finding himself busy, though, beating out Marco Bresciano's early shot and then thwarting Cristian Zaccardo's far post header.
On the hour, the diving Cole threw himself at Jonathan Spector's hanging cross, but after sending his header on to Fontana's right-hand post he landed awkwardly and was stretchered off.
Within seconds of that mishap, the visitors UEFA hopes were extinguished by Simplicio, who calmly lobbed the ball over the hopelessly exposed Carroll, after Di Michele robbed the dithering Gabbidon and sent the Brazilian galloping away.
And on 67 minutes, Di Michele raced clear of the pushed-up West Ham rearguard and slotted between the helpless keeper and his left-hand upright.
Alan Pardew immediately replaced Javier Mascherano and Harewood with Teddy Sheringham and Yossi Benayoun but, by now, the hapless Hammers were already putting their passports away for another year.