Gouveia birdied seven of his first nine holes at The International in Amsterdam and looked on track to push for a 59 until a 90-minute storm delay checked his momentum, leaving him to settle for a seven-under-par 64.
The 33-year-old still described it as "the best round of my life so far" but he was just one shot ahead of Syme after the Scot took advantage of the rain-softened greens to post a 66 featuring eight birdies and two bogeys.
Syme said of the delay: "I think we (the later starters) definitely got a little bit of a break with it - it was still tricky with the rain but I felt like there were a few shots where the greens had softened up a bit, a few pins we were able to get at that we might not have been able to this morning.
"It was nice to take advantage of that and hit some really quality shots."
Compatriot Richie Ramsay made five birdies and a hole-out eagle in six holes from the third to leave himself a further shot back alongside England's Dan Brown, who had an eagle of his own at the eighth.
Both players were coming off recent absences and Ramsay, playing in his first event since recovering from a virus he picked up in China in April, said: "It was nice to feel competitive as I sort of missed that.
"I just tried to enjoy it and it is a course I do enjoy because there is wind and you have to hit lots of different shots and need to hit the ball straight."
Brown said: "It's been a while, I had seven or eight weeks off struggling with my knee.
"Didn't really have much coming in, played terribly yesterday in the pro-am and got quite lucky, found something in the warm-up after the delay."
The group at five under also included Frenchman Pierre Pineau, American John Catlin, Germany's Max Kieffer and Swede Joakim Lagergren.
Australia's Jason Scrivener was on three-under, four shots off the lead, but there was little to cheer for compatriot David Micheluzzi, who finished with a five over 76, and Danny List who was a further shot adrift. Daniel Gale carded a 12-over 83.
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