Markus Brier collected seven birdies and one bogey for a 66 at Le Meridien Moscow Country Club to share third place with Euan Little at 9-under-par 135. Little carded a 4-under 68 in Friday's second round.
Nystrom, who has made seven of nine cuts on the European Tour this season, picked up his first birdie of the day at the par-5 second and added another birdie at the par-3 fourth.
The 35-year-old then ran off back-to-back birdies from the sixth to reach 8 under and continued his charge on the front nine with a birdie at the ninth. Nystrom made it two in a row again with a birdie at the par-4 10th, but cooled down from that point on with pars on each of his last eight holes.
'It was a little strange today because I putted so well on the front nine and holed a few long putts and then the back nine was the opposite where I started to hit the ball very close but did not hole anything,' said Nystrom, who shot a 66 on Friday. 'That was a little bit infuriating.'
After opening with a blistering 63, Baraka got off to a slow start on Friday with a bogey at the third, his first dropped shot of the tournament. Baraka recovered well with two straight birdies starting at the fourth, but gave those shots back with a pair of bogeys around the turn.
The 26-year-old, who is the nephew of European Ryder Cup captain Bernhard Langer, battled back with a birdie at the 13th before a birdie at the 15th assured him of a piece of the 36-hole lead.
'I have actually spoken to Bernhard about being in this position before and he told me not to look at the leaderboard because anything that is on the leaderboard puts you under pressure,' said Baraka, who is looking for his first career victory on the European Tour. 'I think that's the way Bernhard does it. Well, I don't think that he would tell me that if he didn't believe in it himself. But what does he know? He's only won about 70 times in his career with some majors and Ryder Cups in there as well.'
Gary Emerson fired a 65 to move into a tie for fifth place at 8-under-par 136 along with Roope Kakko, David Griffiths, Alvaro Salto, Mattias Eliasson and Alexandre Balicki.
Matthew King was one shot further back at 7-under-par 137.
The 36-hole cut fell at 2-under-par 142 with 70 players qualifying for the weekend.