The 19-year-old took the lead from Lesotho's Tsepo Ramonene Mathibelle on the 36km mark and saw off pressure from Ethiopian Yemane Tsegay for a memorable win at Beijing's iconic Bird's Nest stadium.
Ghebreslassie, racing just his third marathon, clocked 2hr 12min 27sec, with Tsegay, fourth in 2009 and eighth in Moscow two years ago, taking silver in 2:13.07 and Munyo Solomon Mutai of Uganda claiming bronze (2:13.29).
It was Eritrea's second ever world medal after Tadesse Zersenay's silver in the 10,000m in the 2009 worlds in Berlin.
The runners swept through the 10km mark in 31:51, and a surge through the following 5km saw the pack string out with Dechasa up front, Uganda's defending champion Stephen Kiprotich just 5sec off the pace in the chasing pack.
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A definitive break predictably saw the Ethiopian trio of Lelisa Desisa, Tsegay and Berhanu Lemi, Ugandans Kiprotich, Mutai and Jackson Kiprop, and Kenyan trio Dennis Kimetto -- the world record holder, Wilson Kipsang and Mark Korir all eyeing each other up.
Meucci, the 2014 European marathon champion, went through 20km in 1:03.23, teammate Rugero Pertile taking up the running.
The Italian duo struck out on their own, but were sucked in on the 25km mark, Lesotho's Mathibelle sprinting away after 90 minutes of running and building up a 25-sec lead.
Ghebreslassie set out after Mathibelle, overtaking the flagging Lesothan on the 36km mark.
The duo were neck-and-neck as the approached the Bird's Nest, but Ghebreslassie produced one last kick, punching the air and snatching his country's flag as he entered the stadium for the final 100 metres.
There was no luck for Kiprotich, who missed out an unprecedented three consecutive global championship marathons after previously winning golds at the London Olympics and the Moscow worlds.
The Ugandan eventually finished sixth (2:14.42), with Kenya's Kimetto, the world record holder after setting 2:02:57 in Berlin last year, pulling up after 1:38.