Murray won the first set 6-2 on centre court at Wimbledon.
And despite a spirited effort from Nieminen, he could not stop Murray advancing, with the British number one taking the second set 6-4 to go through in straight sets.
"I lost concentration a bit at the end of the second set, I had a few chances to go up a couple of breaks and I missed a few shots but I played well, I started the match off well," said Murray.
"When you play in front of packed crowds it helps. When it's home support and it's with you it helps, it helps a lot.
“The atmosphere has been great since the first match of the tennis. Hopefully I can keep going because it's fun to play in an atmosphere like this.
"A lot of people are just expecting us to do well because it's a home Olympics. In Beijing the GB team did unbelievably well.
“To play in front of a home crowd is different. Support helps, it makes a big difference, but it also adds pressure."
Murray – who faces Marcos Baghdatis in the men’s last 16 after the Cypriot knocked out France's Richard Gasquet 6-4 6-4 – and 18-year-old Robson will team up again in the mixed doubles at the London 2012 Olympics.
The pair, who were handed a wildcard by the International Tennis Federation, have played together at the Hopman Cup in Australia, reaching the final in 2010.
Returning to the Games after an 88-year absence, the mixed doubles tournament will see 16 pairs from 13 countries battle it out for gold.
Wimbledon champions Lisa Raymond and Mike Bryan of the United States face Italy's Sara Errani and Andreas Seppi while two-time grand slam champions Liezel Huber and Bob Bryan, seeded two, take on Germany's Sabine Lisicki and Christopher Kas.
The United States were the last country to win the mixed doubles when Richard Williams, a survivor of the Titanic disaster, and his partner Hazel Wightman took home the gold at Paris in 1924.
Tennis was removed as an Olympic sport after Paris, only returning in Seoul 1988, but without the mixed doubles.
Czech Republic pair Radek Stepanek and Lucie Hradecka await the British duo in the event tomorrow.
"He will have the upper hand against me, but you know I will just go out there and give it a try, you never know," world number 44 Baghdatis, who kissed the court in celebration after his second round win, said of his upcoming clash against Murray.
"I am in the 16's of an Olympic event and that's an incredible thing for me and I hope I will keep going."
Meanwhile, Novak Djokovic barely broke sweat to dismiss former grand slam winner Andy Roddick 6-2 6-1 in less than an hour as he continued his quest to better his Beijing bronze medal.
Second seed Djokovic, already out of the doubles after he and Viktor Troicki lost their opening match to Sweden's Johan Brunstrom and Robert Lindstedt, at one point won seven successive games against his American opponent, sporting stars and stripes trainers.
"Today everything was working perfectly well and I was neutralising his serve by getting a lot of returns back in the court and serving a lot of aces," said 25-year-old Djokovic.
"You're not playing for yourself like you are most of the time throughout the year. This is one of the unique events, unique opportunities to play for your country and the nation is cheering for you."
American Venus Williams, due to play doubles later with sister Serena, marched through her second round match against Canada's Aleksandra Wozniak with a 6-1 6-3 win before stopping at the side of the court to swap Olympic Committee pins with two journalists from the Bahamas.