KL Rahul made 79 but LSG failed to chase down the 208-run target in Eliminator.
The skipper praised Rajat's brilliant century in the decisive game.
A fan breached security and ran towards Kohli to meet him, but police got to him first.
The Women in Blue have been out of action after the ICC Women's World Cup 2022.
The entire tournament will be played in Pune.
Kohli made 25 runs in RCB's win over LSG in the Eliminator match.
RCB won the match by 14 runs and will play RR in Qualifier 2 in IPL 2022.