The third seed admitted after the match he knew little of his opponent, having to check the internet at the weekend to ensure he was the player he thought he was.
But his lack of knowledge meant little on court, as Federer breezed to a 7-5 6-2 6-2 victory in little over an hour and half.
It was a welcome result for Federer who pulled out of the Qatar Open 10 days ago with a back injury.
"It's no problem, I'm happy to be 100 per cent fit," he said in his post-match court-side interview. "I've been this way for three or four days. It's a good thing."
An energetic Kudryavtsev almost took Federer to a tie-break in the opening set, but the Swiss broke at 6-5 and never really let up from that point on.
A moment of complacency saw him allow Kudryavtsev to level at 30-30 in the first game of the second set, but any hopes the Russian had that maybe the heat had got to Federer were dashed when the Swiss powered an ace down the centre to set up the game-winning point.
He broke twice to take the set and a tricky shot through his legs, on a dead ball, garnered as much applause as anything else as he eased to victory.