Did L win against Light?
It really depends on what you call winning.


L had been suspicious, strongly suspicious and just a tad less strongly suspicious of Light being Kira throughout the entire anime (or, well: those potions wherein he was alive).
L, however, wanted to prove that Light was Kira with evidence that would suffice to try him guilty. Collecting enough evidence to win a court case was also the police task force’s goal. They never achieved that or they would have arrested (and subsequently tried) Light.


In games like the board game Cluedo (or Clue, if you’re on the other side of the pond), you can essentially win by guessing correctly. In crime fiction or real-world criminal investigations, you don’t win by guessing correctly, you only win by proving you’re correct. Thus, applying the rules of Cluedo, L won; but he himself wouldn’t have considered him winning due to thinking in criminal investigation terms.



Since you now clarified what you mean by winning:

L did not win the mind game. We was on a good track, but he was short of the goal. If Rem hadn’t taken action, it probably wouldn’t have been too long before L had proven to himself that Light is Kira, at which point he would have also told the world about it. However, he was stopped just short of proof.