Fourth seed Myneni played smartly to dispatch his Australian rival 6-3 6-4 in the men's singles second round of the USD 50,000 ATP Challenger event.
Myneni served well, which always has been his strength, and had a tight grip over the contest that was over in one hour at DLTA.
The Aussie matched Myneni in terms of power but Myneni had better control over his strokes as he went about his business calmly. He broke Barton in the sixth game of the first set and ninth of the second to seal the match.
The tall Indian said he wants to improve his ranking so that he can be in reckoning when the national team is selected for the Olympics.
"It's a long way to go. I need to move up to be there."
Myneni next plays China's Zhe Li, who came from behind to end the run of Indian qualifier Vishnu Vardhan 3-6 6-3 6-3.
Ankita said the court was fast and the balls were very light, causing the ball to fly.
Marina hardly posed a challenge to Ankita, losing her first six service games and as a result she was trailing 1-6
1-4 at one stage.
Ankita dropped serve in the sixth game of the second and eighth to allow the Russian make it 4-4. However the Indian exploited the never-ending errors of her rival to break her in the ninth game and serve out the match in the next.
The 23-year-old said her win over world number 56 Nao Hibino in the Fed Cup has boosted her confidence.
Meanwhile, wild card entrant Karman Kaur Thandi was ousted by Taipei Ya Husan Lee 3-6 4-6 in another second round contest and Mihika Yadav lost 2-6 2-6 to Thailand's Kamonwan Buayam.
Ankita is now the only Indian left in the singles draw and her next rival is also from Russia, Anna Morgina, who battled past French girl Reix Sherazad 6-3 6-7(3) 6-3.
