The former world number one dispatched the 20-year-old in one hour and 38 minutes to seal his spot in the semi-final.
Both players had to contend with blustery conditions but ultimately it was the three-time Grand Slam winner who prevailed 6-4 7-6.
The 35-year-old is looking to win his first title on grass in six years and will take on American Denis Kudla for a place in the final.
"The conditions were tricky, it was a bit blustery," said Murray on court. "There was some old-school grass court tennis out here.
"I enjoy it here, but it is different to Wimbledon and Queen's, in terms of the way the court plays.
"It's a lot quicker here and there's not many opportunities to break serve. I had to stay strong at the end of the second set."
Nakashima, who was the fifth seed at the tournament, joined Gijs Brouwer and Jurij Rodionov on the list of players who failed to take a set off Murray at the event.
The Olympic gold medallist opted to take part at Surbiton and miss the French Open in order to better prepare for this year's Wimbledon.
The Brit has endured a number of injury battles over the years, but the player is determined to have another serious run at SW19.
Elsewhere at the Surbiton Trophy
Jordan Thompson, who bowed out in the opening round of the French Open against Rafael Nadal, also booked his place in the semi-final with a straight sets win over Christopher O'Connell.
The Aussie will face Finland's Otto Virtanen who beat Britain's Ryan Peniston over three sets.
Denis Kudla, who takes on Murray in the semi-final, also enjoyed a 6-4 7-6 win over Australia's Max Purcell.