Murray looked in great shape as he dropped six games in a straight sets victory on Centre Court.
Murray raced into a 4-1 lead in the opening set and with the break under his belt he was never really challenged in the opening exchanges.
Into the second set Nieminen did put up more of a fight but it was not enough as Murray wrapped up a 6-2 6-4 victory.
And Murray revealed how much he is enjoying the atmosphere when he spoke to the BBC after the match: "When you play in front of packed crowds it helps. When it's home support and it's with you it helps a lot.
"The atmosphere has been great since the first match. Hopefully I can keep going because it's fun to play in an atmosphere like this."
Murray will now face Marcos Baghdatis in the third round just weeks after their encounter at the same point at Wimbledon.
The Cypriot, who carried the flag for his country, saw off Richard Gasquet 6-4 6-4 to reach the third round.
There was also a win for Novak Djokovic as he lost just as he thrashed Andy Roddick 6-2 6-1 in their second round clash.
While Roddick did play well Djokovic was just too strong on the baseline and the American was unable to threaten.
There was also a great win for Aussie Lleyton Hewitt as he rolled back the years with an impressive 6-4 7-5 win over Marin Cilic.
Cilic was the thirteenth seed in the competition but former world number one Hewitt has battled back from injury and surgery to once again play for his country.
FemaleFirst Helen Earnshaw
by Helen Earnshaw
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