The world number four Indian had to toil hard before prevailing over two-time All England champion Tine 21-13, 21-23, 21-13 in a women singles quarterfinal match which lasted a little less than an hour.
The 21-year-old Saina kept the pressure on her rival and played a lot of smashes, but she gained more points with her dribbling at the net.
In the first game, Saina opened up a narrow lead after 5-5 but Tine kept breathing down her neck at 9-10 before the Indian started reeling off straight points to widen the gap and take a 1-0 lead.
Not ready to lie low, Tine raced to a three-point lead in the second game but straight six points helped Saina to zoom past her and take a 14-10 lead.
However, the Dane refused to give up and caught up with the Indian at 15-15 and held on to win the second game and draw level.
In the decider, Tine again managed to open up a narrow two-point lead early but Saina soon gathered herself and grabbed a 9-7 lead to keep the pressure intact. She soon raced to a win in the game and the match.
In the semifinals on Saturday, Saina will take on the winner between top seed and world number one Chinese Yihan Wang and Xuerui Li.