The unseeded Serb who beat Andy Roddick in the second round, won 7-6 (7-1) 7-6 (7-3) 6-4 to reach the last 16.
Fierce service games led to tie-breaks in the first two sets, and a Tursunov double fault helped Tipsarevic win the opener on Court Two.
An ace sealed the second and Tipsarevic held off a Tursunov fightback to take the third with another ace - his 13th.
Tipsarevic, 24, said: "I am proud of myself because I managed to do something which I usually don't, which is beat a big name and then continue playing with the same intensity and have comfortable win in the next round."
The world number 40 now faces Germany's Rainer Schuettler, who beat Guillermo Garcia-Lopez of Spain 6-2 6-3 6-4.
Schuettler, 32, once ranked as high as world number five but currently down at 94, is the oldest man left in the draw.
An Australian Open finalist in 2003, he beat ninth seed James Blake in five sets to reach the third round and has now matched his best run at Wimbledon five years ago.
Asked if he had considering retirement following his fall down the rankings due to injury and illness, Schuettler said: "Yes, a couple of times.
"I had glandular fever and because I'm was desperate to play again, I didn't give myself time to recover.
"There were times when I really thought maybe I should look for something else. But, at the end of the day, I do what I love, what I enjoy, and that's the most important thing."
Arnaud Clement triumphed in another battle between unseeded players, with the Frenchman beating Austria's Jurgen Melzer 4-6 6-3 6-4 6-4.
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