Rubin forward Alejandro Dominguez stunned the Italian champions with a great solo effort in the 11th minute when he evaded several Inter defenders before beating Julio Cesar with a rising shot into the roof of the net.
Dejan Stankovic equalised 16 minutes later when he was left unmarked to head in Maicon's cross at the far post past stranded Rubin keeper Sergei Ryzhikov.
A couple of minutes later, Mario Balotelli could have given the visitors the lead but his long-range curving shot hit the crossbar.
However, Inter, who had Balotelli sent off on the hour for a second yellow card, were lucky to leave Kazan with a point after the Russians missed a host of chances late in the game.
Rubin captain Sergei Semak wasted their best chance, hitting the post from six metres nine minutes from time.
TORMENTING DOMINGUEZ
Argentine Dominguez, the most threatening Rubin player who also scored for the Russian champions in a 3-1 defeat at Dynamo Kiev two weeks ago, tormented the Inter defence before he was substituted with four minutes left.
At the other end, Samuel Eto'o, who joined Inter from Barcelona in the close season in a swap deal for Zlatan Ibrahimovic, had a poor game.
The Cameroon striker created little danger around the Rubin goal after missing a good chance early in the match when he could not force his effort past Ryzhikov from close range.
Rubin coach Kurban Berdyev was left to rue his team's missed chances.
"I feel that we lost two points tonight rather than gained one," he told Russian television NTV.
"We dominated the game after Inter were reduced to 10 men, but unfortunately just couldn't capitalise on our chances."
Inter coach Jose Mourinho told Sky television: "Given the circumstances of the game, it is a point gained.
"Our opponents started better, they pressed and had their fans urging them on as it was their home debut."
The draw extended Inter's winless streak in the Champions League to seven matches following their 0-0 stalemate with Barcelona in their Group F opener two weeks ago.
