Federer, showing flashes of brilliance mixed with occasional errors, closed out in just over an hour to win the second round match 6-2 7-5.
The 17-time Grand Slam winner was making his first appearance in Turkey at the Istanbul Open, the first ever ATP world tour event in the country.
Federer, who is seeded to meet world number 11 Grigor Dimitrov of Bulgaria in the final, is hoping to use the clay court event to fine tune his bid for a second French Open title next month.
He is looking for confidence on the slower clay, after a long hard court season, having lost in the third round on clay to Gael Monfils at the Monte Carlo Masters this month.
Federer raced through the first set in just 20 minutes, pulling out his full armoury of drop shots, cross court forehands and backhand winners against a clearly hesitant Nieminen, the world 71.
A stunning drop shot from Federer that fell dead inside the service court broke Nieminen's serve in the fifth game and left the crowd gasping.
The crowd, who had braved heavy evening traffic to catch Federer play at the 8,000-capacity Garanti Koza arena on the outskirts of Istanbul, began to get behind the Finn to prolong the game.
Nieminen showed greater confidence in the second set, holding his serve with ease and an over-relaxed Federer spraying the ball wide regularly.
The Federer forehand was responsible for a string of unforced errors, allowing Nieminen to hold serve without trouble.
But Federer, serving and volleying on occasion and delivering nine aces in the match, found his top gear at the close of the set.
Piling pressure on the Nieminen second serve and using his trademark drive volley to great effect, Federer finally broke Nieminen to lead 6-5.
He then served out to love, finishing with a stunning backhand cross court that left Nieminen with arms and legs akimbo.
In Friday's quarterfinals, Federer will face Daniel Gimeno-Traver of Spain, who overcame Kazakhstan's Mikhail Kukushkin in straight sets.
Dimitrov meanwhile is due to start his campaign against Andrey Golubev of Kazakhstan on Thursday.
Fourth seed Santiago Giraldo of Colombia went through to the quarters with a tough 6-4, 1-6, 6-3 win against Andrey Rublev of Russia.
TENNIS
Federer heads to quarters in Istanbul Open
World number two Roger Federer on Wednesday eased past fellow 33-year old, the Finn Jarkko Nieminen, with a dominant display to reach the quarterfinals of the Istanbul Open tennis tournament.
ROGER FEDERER
Is this the end of the road for Swiss tennis legend Roger Federer?
Roger Federer is talking optimistically about returning to his "highest level" after knee surgery, but does tennis have to start adjusting to a future without the Swiss star?
The 20-time Grand Slam winner announced on Wednesday that he would be sidelined until 2021 after his second operation in a matter of months.
Federer remains upbeat, tweeting: “I plan to take the necessary time to be 100 percent ready to play at my highest level.”
In some ways 2020 is a good season to miss after the coronavirus ravaged the tennis schedule. Writing Federer off in the past has proved dangerous.
He returned from a six-month injury lay-off to claim the Australian Open in 2017, winning his eighth Wimbledon crown later that year.
But he will be 40 in 2021 and is now heading into uncharted territory.
Despite his groaning trophy cabinet, there are two factors that will motivate Federer to keep going — the risk of losing his grip on the men's Grand Slam title record and a missing Olympics singles gold medal.
Rafael Nadal has 19 majors, just one shy of Federer's mark and Djokovic has 17.
Spain's Nadal will be fancied to draw level with Federer at the French Open, rescheduled for September, while few would bet against Djokovic winning in New York weeks earlier.
In April, Federer said he was “devastated” when Wimbledon was cancelled for the first time since World War II. Last year he fell agonisingly short at the All England Club, failing to convert two championship points on his own serve against Djokovic.
The Wimbledon grass probably remains his best chance of adding to his Grand Slam collection — he has not won the US Open since 2008 and his only title at Roland Garros came in 2009.
Even though Federer has slipped from the very pinnacle of the game, he is still a major threat to Nadal and Djokovic.
'Golden' ambitions
Last year, the world number four had a 53-10 win-loss record and he reached the semi-finals at the Australian Open in January in his only tournament this year.
Federer, who is still six ATP titles short of Jimmy Connors' all-time record of 109, has one glaring omission from his CV — the Olympic title.
The Swiss won doubles gold in Beijing in 2008 with compatriot Stan Wawrinka but lost in the singles final to Andy Murray in London four years later.
The postponed Tokyo Games will almost certainly be Federer's last opportunity to complete a career “golden” Grand Slam — he will turn 40 on the day of the closing ceremony next year.
Tennis will feel the loss of the elegant Federer keenly when he walks off the court for the last time.
Djokovic and Nadal have been the dominant forces in recent years but the Swiss remains the biggest draw and last month topped Forbes' list of the world's highest-earning athletes.
His last appearance on court was in front of nearly 52,000 fans — touted by organisers as a world record for tennis — at a charity match against Nadal in Cape Town in February.
Federer is nearly always the crowd favourite wherever he plays and has proved a perfect ambassador for the sport since he won his first Grand Slam title in 2003.
He certainly expects to be back and competitive next year.
“I will be missing my fans and the tour dearly but I will look forward to seeing everyone back on tour at the start of the 2021 season,” he tweeted.
The avalanche of support from his adoring fans showed they would miss him too, but they will have to get used to a time when he is gone for good.
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