The seventh seeded Russian, playing her first match since February, said she had considered walking away from the game after suffering a stress fracture of three ribs while working with a new physical trainer in Moscow.
She felt so out of shape when it was time to begin her comeback that she considered whether she really wanted to make the effort.
"It was a very disappointing and tough time for me," Dementieva told reporters. "I couldn't really do anything and it was time for me to think what I want to do in my life and did I want to come back or do something else.
"I'm not that young. I'm 25 years old, and when something like that happens it's really difficult to start practising after not playing for six weeks.
"I was not able to even go for a little run and I completely lost almost everything. For me it was like starting at the beginning, playing against the wall on my first practice. It was really difficult."
The conditions did nothing to inspire the players, who both wore long sleeves and trousers throughout the two hour and 40 minute battle.
Only two games went with serve in the opening set, but Dementieva looked more positive in the second and allowed Tu just one game point.
Both players held break point opportunities early in the final set, and from 2-2 the next six games went against serve.
Tu was broken as she served for the match at 5-4, and in a tense finale Dementieva fought off two break points to hold for 6-5 before clinching victory on her second match point.
"It was freezing out there and I've never played with snow in my life," said Dementieva. "There were ups and downs, but I'm glad I was able to go through a difficult match and difficult moments and win in the end."
Dementieva now awaits another potentially gruelling challenge with Venus Williams, although the unseeded American first has to overcome Michaella Krajicek of the Netherlands. That match was postponed until Wednesday because of failing light.
Top seed Justine Henin will play Anna-Lena Groenefeld after the German beat Estonian Kaia Kanepi 6-2 6-4, and defending champion Kim Clijsters will tackle Ukrainian qualifier Julia Vakulenko, who overwhelmed Russia's Elena Likhovtseva 6-4 6-1.
Third seed Svetlana Kuznetsova of Russia plays Ukraine's Kateryna Bondarenko, who beat Austrian teenager Tamira Paszek 6-1 6-7 6-1 in a battle between two qualifiers.
Fourth seeded Serb Jelena Jankovic plays Elena Vesina of Russia, a 2-6 7-6 6-3 winner over Polish wild card Urszula Radwanska.
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