The world no.5 won 21-4, 21-14 in just 24 minutes in the group E match at the Wembley Arena.
It was easy going for the Indian in the first game, while complacency got the better of her in the second as Tan, ranked 45, made a valiant effort.
Saina will play the winner of Group F for a place in the quarterfinals.
Jwala and Ashwini won their first match in the tournament to keep their hopes alive of making it to the knockout round.
The pair beat Chinese Taipei's Wen Hsing Cheng and Yu Chin Chien 25-22, 16-21, 21-18 in a group B match in 55 minutes.
Jwala and Ashwini made a fast start surging to an 11-6 lead but some loose play by the duo allowed their opponents to comeback into the game. With the game being tied at 21-21, the Indians won some crucial points to wrap up the game.
The second was a one-sided game as Cheng and Chien led from start to end. The decider was a hotly contested affair. The lndians though always held a narrow lead against their opponents and finally finished the match with some good net play.
Jwala and Ashwini's fate will be decided on Tuesday when they take on Singapore pair Shinta Mulia Sari and Lei Yao.