The Turkish side started ferociously in front of a partisan home crowd and took a deserved lead inside the opening 10 minutes when Cape Verde international Rodrigues scored from distance.
Lokomotiv twice came close to equalising through Solomon Kvirkvelia and Jefferson Farfan as Galatasaray looked like they might be punished for failing to double down on their early dominance.
Derdiyok had other ideas, though, whipping in a superb free-kick from 25 yards in the 67th minute before Inan netted a penalty in stoppage time after Emre Akbaba had been brought down in the area.
Not even the late dismissal of Badou Ndiaye for two bookings could take the shine off a fine night for Fatih Terim's side, who open their Champions League campaign with a flourish.
The hosts started with a spring in their step and opened the scoring after nine minutes when Rodrigues' low shot from outside the penalty area powered through Guilherme's less-than robust resistance.
The Russian champions recovered well and carved out a number of opportunities as the first half wore on. Kvirkvelia saw a close-range effort cleared off the line and then an unmarked Farfan headed over from six yards when it looked easier to score.
The sides exchanged quick-fire chances shortly after the restart, Aleksey Miranchuk's fizzing effort palmed away by Fernando Muslera and Guilherme tipping over Ndiaye's thunderous drive from 30 yards.
There was little Guilherme could do about Galatasaray's second, though, as Derdiyok's free-kick found the net.
Ndiaye received his marching orders three minutes from time for a rash second booking, but that did not stop the hosts adding a third deep into added time from the spot after Guilherme tripped Akbaba to abruptly end a flowing counter-attack.
What it means: Galatasaray in pole position
Schalke and Porto's draw in Germany means Galatasaray are sitting pretty at the top of Group D. There is a long way to go, of course, but three points on the board already sets them up for their remaining games. Rock-bottom Lokomotiv, meanwhile, need a drastic improvement if they are to kick-start their already stuttering campaign.
Pat on the back: Rodrigues on fire
The scorer of Galatasaray's first was in imperious form throughout, causing no end of problems for Lokomotiv's backline. His opener was a deserved reward for an all-action display and his only disappointment will be that he did not score more.
Boot up the backside: Guilherme endures difficult outing
The Lokomotiv goalkeeper's outing got off to a bad start, letting Rodrigues' early effort slip through his grasp, and he never recovered. His foul on Akbaba for the late penalty was a fitting end to a torrid game for the 32-year-old.
Key Opta stats:
- Rodrigues became just the third player from Cape Verde Islands to score a Champions League goal after Cabral and Ze Luis.
- Derdiyok is the first Swiss player to score for three different clubs in the Champions League (Bayer Leverkusen, Basel and Galatasaray).
- Rodrigues scored the fastest home goal for Galatasaray in Champions League history (08:40). The record was previously held by Felipe Melo with his goal against FC Copenhagen in October 2013 (08:59).
- Galatasaray are the first Turkish side to beat a side from Russia in the Champions League since December 2007, when Fenerbache won 3-1 against CSKA Moscow.
- Lokomotiv have still never won their opening match of a Champions League campaign (D1 L3).
Galatasaray travel to Portugal to face Porto next in Europe, while Lokomotiv welcome Schalke to the Russian capital.