Judge Tudor Owen ordered Blagrove, 34, jailed for two years. Burton, 22, received two years' community service.
Prosecutors say the pair covertly filmed Winehouse at a party and sold the footage to The Sun newspaper for 50,000 pounds ($75,000). In January the paper published the images, which appeared to show the singer smoking crack cocaine and snorting a substance from a card.
Detectives decided there was not enough evidence to charge Winehouse because it could not be proved what the substances were. But they charged the couple with offering to supply drugs.
Police who raided Blagrove and Burton's home found a list of celebrities they planned to film taking drugs, including Winehouse. The judge said there was no evidence they actually sold the singer drugs — a fact that saved them from longer sentences.
"Notwithstanding what is clearly visible in the video, there is no evidence of drugs being supplied or even used," he said.