Sainz took the lead of the race on the opening lap as he slipstreamed former McLaren teammate Lando Norris down into Turn 1.
The Spaniard was one of the first drivers to stop for hards, losing ground to the leaders when he encountered traffic.
At this point, Sainz was told by Ferrari over team radio that he was on course to finish fifth.
Reflecting on his race in Russia, he said: “Quite a lot [of pleasure], mainly because at one point in the race it really looked like it was going wrong. After suffering so much graining with the Medium tyre, after leading the race quite comfortably for the first seven or eight, there was so much degradation and I lost the position to Lando. I was one of the first ones to pit, got it the queue behind Valtteri and suffering with all that traffic.
“At some point I really thought the podium was not happening, but I found myself in P3, in front of Pérez, some ten laps from the end, so I said to myself, “now it’s a good opportunity to keep this position.”
Sainz revealed that he considered making a second stop for soft tyres due to how much he was struggling before the rain hit in Sochi.
“I had good pace with the hards, I found a good feeling, but then I saw the rain coming, it was starting to rain in Turns 5 and 7 and all of us out there on hards we were all struggling massively to keep the car on track, while people on mediums they looked to be having a bit more grip, they looked that with the softer tyre they were managing to keep their cars on track, I was just nowhere,” Sainz added.
“I was, at some point, considering to pit for the soft tyre, just to make it to the end and, in the end, we decided to go for inters for the last four laps and it worked out beautifully. We ended up third. Good calls, good management, just a bit more obstacles than I expected after leading the race.”