Goalkeeper Kouakou Koffi pushed a Cheikhou Dieng cross into the path of Seydi from French second-tier club Metz and he made no mistake from close range.
Senegal, who were winning the quadrennial tournament now confined to under-23 footballers for the first time, created more chances thereafter at Stade Alphonse Massamba Debat, but there were no more goals.
The best previous performance by the Senegalese was fourth four years ago in Mozambique while the Burkinabe did not make the knockout stage in their other appearance 42 years ago.
Burkina Faso had a genuine first-half penalty appeal rejected after El Hadji Diaw appeared to foul Abdoul Nikiema from behind inside the box.
The losers gained plenty of second-half possession, but wild shooting and a commanding performance by Senegal goalkeeper and captain Pape Ndiaye prevented an equaliser.
Cameroon won four of the past 10 African Games football tournaments, Egypt two, and Algeria, Congo Brazzaville, Ghana and Nigeria once each.