Fraile finished in a time of four hours 23 minutes 14 seconds with Colombian Nairo Quintana, second overall, in the same group as Dumoulin on Wednesday.
Britain's Orica rider Adam Yates was also in the group that finished one minute 37 seconds behind Fraile.
Wales' Geraint Thomas, second in Tuesday's time trial, dropped to 14th overall - six minutes 21 seconds back.
The Team Sky rider was unable to stick with the leaders in the last climb of the hilly 161km stage from Florence to Bagno di Romagna.
Fraile was part of the breakaway and edged a long chase to the finish for Dimension Data's first win in the Giro.
Thursday's stage 12 is a mostly flat, 234km run from Forli to Reggio Emilia.
1. Omar Fraile (Spa/Dimension Data) 4hrs 23mins 14secs
2. Rui Costa (Por/UAE Team Emirates) Same time
3. Pierre Rolland (Fra/Cannondale)
4. Tanel Kangert (Est/Astana)
5. Giovanni Visconti (Ita/Bahrain)
6. Ben Hermans (Bel/BMC Racing)
7. Dario Cataldo (Ita/Astana)
8. Simone Petilli (Ita/UAE Team Emirates)
9. Maxime Monfort (Bel/Lotto) +3secs
10. Laurens De Plus (Bel/Quick-Step) Same time
1. Tom Dumoulin (Ned/Sunweb) 47hrs 22mins 07secs
2. Nairo Quintana (Col/Movistar) +2mins 23secs
3. Bauke Mollema (Ned/Trek) +2mins 38secs
4. Thibaut Pinot (Fra/FDJ) +2mins 40secs
5. Vincenzo Nibali (Ita/Bahrain) +2mins 47secs
6. Andrey Amador (Crc/Movistar) +3mins 05secs
7. Bob Jungels (Lux/Quick-Step) +3mins 56secs
8. Tanel Kangert (Est/Astana) +3mins 59secs
9. Domenico Pozzovivo (Ita/AG2R) +4mins 05secs
10. Ilnur Zakarin (Rus/Katusha) +4mins 17secs
Selected others:
14. Geraint Thomas (GB/ Team Sky) +6mins 21secs
16. Adam Yates (GB/Orica) +6mins 58secs
Spain's Omar Fraile won the 11th stage of the Giro d'Italia as Dutchman Tom Dumoulin held on to his overall lead.