Protesters at County Hall in Matlock earlier said the decision puts children's lives at risk.
Some 35 schools will lose their patrol, 19 have had vacant posts scrapped and a further 42 crossing guards will not be replaced if they leave.
The authority said it had chosen the sites carefully and the move would save it Â£320,000 a year.
Councillors approved the plans, despite receiving 28 petitions with a combined total of more than 16,000 signatures against the move.
Protester Lisa Pritchard said it was a "disgrace" that the authority had disregarded people's opinions.
"There's going to be an accident because the children rely on the services of the lollipop people," she said.
The council said the move was better than an original proposal to scrap all 189 patrols in Derbyshire and said it had little choice but to cut "non-statutory" services if it is to save Â£160m in the next five years.
Cabinet member for highways Dean Collins said the 35 sites that have lost their patrol were chosen because they have zebra or pelican crossings nearby.
"We can't keep providing non-statutory services at the level that we do," he said.
The patrols are likely to be axed in November or December, the council said.
Almost 100 schools in Derbyshire could be without a crossing patrol if cost-cutting plans are approved.