The top seed battered 18-year-old qualifier Jackson with her thundering groundstrokes to snare the first set in 17 scorching minutes.
Wimbledon 2005: Complete coverage
The teenager had the audacity to break the 1999 champion early in the second, Davenport quickly reasserted her authority.
Pounding away from the baseline, the world number one broke Jackson for the third time in the set and booked her place in the last 32 against either Russian 30th seed Dinara Safina or Czech Barbora Strycova.
Results from the Wimbledon Women's Singles Round 2 matches on Wednesday
Magdalena Maleeva (Bulgaria) beat Maria Kirilenko (Russia) 6-2 6-3
30-Dinara Safina (Russia) beat Barbora Strycova (Czech Republic) 6-2 6-2
6-Elena Dementieva (Russia) beat Sabine Klaschka (Germany) 2-6 6-3 8-6
5-Svetlana Kuznetsova (Russia) beat Sania Mirza (India) 6-4 6-7(4) 6-4
1-Lindsay Davenport (United States) beat Jamea Jackson (United States) 6-0 6-3
Mashona Washington (United States) beat Selima Sfar (Tunisia) 6-3 3-6 6-3
13-Elena Likhovtseva (Russia) beat Meghann Shaughnessy (United States) 6-3 7-6(4)
22-Silvia Farina Elia (Italy) beat Maria Vento-Kabchi (Venezuela) 6-1 5-7 6-3
27-Nicole Vaidisova (Czech Republic) beat Michaela Pastikova (Czech Republic) 7-5 6-3
Shenay Perry (United States) beat Tamarine Tanasugarn (Thailand) 7-6(1) 6-2
3-Amelie Mauresmo (France) beat Maria Sanchez Lorenzo (Spain) 6-1 6-3
17-Jelena Jankovic (Serbia and Montenegro) beat Mariana Diaz-Oliva (Argentina) 6-3 7-5
15-Kim Clijsters (Belgium) beat Marissa Irvin (United States) 6-1 6-1
9-Anastasia Myskina (Russia) beat Aiko Nakamura (Japan) 6-4 6-3
Roberta Vinci (Italy) beat Anne Kremer (Luxembourg) 6-3 6-2
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