Coach Paul Putt said he agonised over including the French-based midfielder in his 23-man squad for the tournament in South Africa as Traore battled to overcome an ankle injury.
But three goals in two games from Traore has put Burkina Faso top of the Group C standings and in touching distance of a quarter-final place.
"He wasn't ready when we had to name our final squad and I waited right up until the deadline to make up my mind," Putt told reporters after his side's 4-0 thumping of Ethiopia in Nelspruit on Friday that included two cracking goals from Traore.
"I was back and forth with the medical people trying to work out whether to take the risk."
Traore, 24, stayed behind in France for treatment when Burkina Faso began their preparations in Ouagadougou just after New Year.
"We sent our doctor over to check on his progress in France but when came to join us he still need several days of rehabilitation. It was less than a week before our first game that he was able to join in with training," Putt said.
Putt kept Traore on the bench for the first match against Nigeria on Monday but he came on to engineer a dramatic comeback, scoring with the last kick of the match to force a 1-1 draw.
"For us that counted as a victory," said the Belgian-born coach.
Traore started against Ethiopia, scoring twice with powerful left-footed shots that are among the best efforts at the tournament to date.
But again Putt said he was not sure about using him.
"He is still not fit, he's had a back problem too and I did not pick him until the medical team promised me he would be fine."
Traore's goals now have the unfancied Burkinabe on the cusp of a quarter-final place after they ended a 17-match winless streak at the finals, stretching back 15 years.
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