Stevens attacked on the final ascent to Montenars after a 111km race to beat Elisa Longo Borghini of Italy and Poland's Katarzyna Niewiadoma.
The American leads Niewiadoma by two seconds in the overall standings.
Britain's world champion Armitstead trails Stevens by three minutes, three seconds with seven stages remaining.
Molly Weaver finished almost four minutes back while fellow Briton Emma Pooley lost 10 minutes, 40 seconds on the stage.
Monday's flatter 120km third stage from Montagnana to Lendinara is expected to suit the sprinters.
Stage two result:
1. Evelyn Stevens (US/Boels/Dolmans) 2hrs 48mins 26secs
2. Elisa Longo Borghini (Ita/Wiggle High5) Same time
3. Katarzyna Niewiadoma (Pol/Raboliv) +2secs
4. Mara Abbott (US/Wiggle High5) +3secs
5. Megan Guaranier (US/Boels Dolmans) +24secs
Selected others:
39. Lizzie Armitstead (GB/Boels/Dolmans +2mins 53secs
41. Molly Weaver (GB/Liv-Plantur) +3mins 48secs
126. Emma Pooley (GB/Lotto Soudal Ladies) +10mins 40secs
General classification after stage two:
1. Evelyn Stevens (US/Boels/Dolmans) 5hrs 29mins 12secs
2. Katarzyna Niewiadoma (Pol/Raboliv) +2secs
3. Megan Guaranier (US/Boels Dolmans) +18secs
4. Elisa Longo Borghini (Ita/Wiggle High5) +23secs
5. Claudia Lichtenberg (Ger/Lotto Soudal Ladies) +35secs
Selected others:
29. Lizzie Armitstead (GB/Boels/Dolmans +3mins 03secs
35. Molly Weaver (GB/Liv-Plantur) +4mins 36secs
90. Emma Pooley (GB/Lotto Soudal Ladies) +11mins 53secs
Lizzie Armitstead finished almost three minutes behind her Boels-Dolmans team-mate Evelyn Stevens, who took the Giro Rosa lead with victory on stage two.