In the 44th minute, the Armenian forward lashed a low, hard shot into the bottom corner of the net after receiving an overhead pass from Luiz Adriano.
Mkhitaryan pounced on a rebound from his own shot in the 76th minute to make no mistake and side-foot the ball into the goal from just inside the area.
This was the first competitive meeting between the two sides, and Shakhtar's first home Champion's League victory in five games.
The sides appeared evenly matched early on but Shakhtar began to control the game and force Nordsjaeland to retreat further and further back, allowing Mkhitaryan to constantly threaten.
Shakhtar had less possession and worse passing statistics but had more shots on target.
"They (Nordsjaelland) were good on counterattacks in the first half," Shakhtar coach Mircea Lucescu said. "But they got tired after the break. I'm pleased with our defense -- the visitors failed to create a single scoring chance."
Defender Ivan Runje was Nordsjealland's most dominant player. He had the Danish side's first shot on target in the first half but couldn't get enough power on a header before goalkeeper Andriy claimed the ball.
"The first hour was OK. But then we had transitions against us," Nordsjaelland coach Kasper Hjulmand said.
"The deciding moments were in the first half. We had good opportunities but the goal before halftime was the deciding moment. We didn't create enough chances but I'm proud of my team -- they played well. But Shakhtar played better."
Shakhtar is unbeaten in 10 consecutive competitive matches this season in the domestic league and in Europe.
"This was my first professional double," Mkhitaryan said. "We needed this victory for confidence in the tournament. It was a difficult match, we did everything possible to ease this match and create as many chances as possible."
Shakhtar midfielder Darijo Srna said the team has learned from last season's last-place finish in the group stage.
"If we don't repeat last year's mistakes then we should advance," he said.
"Furthermore, we have identical chances to advance with Juventus and Chelsea."
Shakhtar leads Group E with Chelsea and Juventus drawing 2-2 at Stamford Bridge in the other match.
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