The ex-Formula One driver, whose career with Renault was ended by injuries sustained in a rally crash in 2011, went quickest on all eight of Friday's stages to leave the rest of the field for dust.
The Polish Citroen DS3 driver is one minute 6.7 seconds ahead of Skoda's Jan Kopecky, who won the season-opening race in Austria. Ireland's Craig Breen is third.
However, Kubica had a scare on the final stage, clipping a wall with the rear of his car. Amazingly, he still managed to post the fastest time.
Kubica said: "It's been a good day. In the last stage there was a tight junction. I pulled the handbrake and touched with the rear a house. I had to reverse and lost 10 or 12 seconds.
"But it’s been a nice day, perfect testing in different weather conditions. Now we just need to continue running at our pace.”
Breen was left to rue a 10-second penalty for leaving the service area too late, after delaying his tyre choice until the last minute on a drizzly day.
He said: "It was a mistake because the car was less precise with more understeer than before. But I’m pleased with my performance and we were able to prove the (Peugeot) 207 is still a competitive car."
RALLY ISLAS CANARIAS - LEG ONE STANDINGS
1 - Robert Kubica (POL) 1:29:32.0
2 - Jan Kopecky (CZE) +01:06.7
3 - Craig Breen (IRL) +01:51.0
4 - Jeremi Ancian (FRA) +02:43.8
5 - Luis Monzon (ESP) +03:36.2
6 - Andreas Aigner (AUT) +04:50.3
7 - Enrique Garcia (ESP) +06:01.8
8 - Germain Bonnefis (FRA) +06:17.4
9 - Joan Vinyes (ESP) +06:39.5
10 - Gorka Antxustegi (ESP) +06:40.1