Dortmund rose to 14th in the Bundesliga standings after their home victory, two positions and two points clear of the relegation zone, although Hertha Berlin (15th, 21 points) and Paderborn (16th, 20) could overhaul Jurgen Klopp's men on Sunday.
But more important to Sahin was the way Dortmund played, claiming they are "on the right track" and returning to the style of play that has brought them so much success under coach Klopp.
"We've taken a huge step forward, particularly in the fact that we played football again and that everyone wanted the ball," the 26-year-old said.
"We didn't just resort to throwing the kitchen sink and hitting it long in the hope that the ball would land at someone's feet. In fact, we earned our luck and played football again."
After a dreadful first half of the season, Dortmund have claimed seven points from four games since the Bundesliga's resumption after the winter break.
That has also coincided in the return of Sahin and Marco Reus to full fitness.
Sahin and Reus did not start a match together in the first half of the campaign due to knee and ankle injuries respectively, but have been in the starting XI in their club's past four fixtures and both scored against Mainz.
"I think I've started the Ruckrunde [second half of the season] quite well," Sahin said.
"I'm fit and at a very good level physically. The coaches and the team are pleased with me, which is the most important thing. I'm comfortable on the field again and not feeling any pain anymore.
"I can go the whole length of a game and throw myself into things. The fact I was rewarded for that with a goal against Mainz will obviously do me good as well."
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