Riverside councillor Phil Hawkins had hoped to oust her as Labour group leader in a secret ballot of Labour's 46 councillors on Monday evening.
Deputy council leader Ralph Cook was challenged by Ramesh Patel but no outcome was reached after presentations by both men and two rounds of voting.
The Labour group are to meet again next week for more voting on the issue.
The balloting took place at the Cardiff Labour group's annual general meeting at County Hall.
Under party rules, council Labour groups are required to either re-elect or replace their leader every year.
Ms Joyce, who represents the Llanrumney ward, has led Cardiff council since Labour took over its running from the previous Liberal Democrat-Plaid Cymru coalition administration after the local elections a year ago.
In a statement, she said: "I am extremely pleased to have been returned as leader again.
"Our first year in office after a disastrous Plaid/LibDem administration has been one of delivery.
"I am hugely looking forward to working with all members of the Labour group to deliver on our manifesto commitments for the people of Cardiff."
Sue Lent was re-elected party chief whip. She had been challenged for the post by Gretta Marshall.
Cardiff council leader Heather Joyce has survived a leadership challenge from within her party.