Atletico struggled to create chances in their final match of a year in which they won the Europa League and continued their resurgence under coach Diego Simeone.
Adrian finally found a way through Celta's defence in the 77th minute when the Spain Under-21 striker sent a snap shot arrowing into the top corner from just outside the area.
Defender Miranda earned a second yellow card for handling the ball and was sent off four minutes from time but Atletico held on to close to within six points of unbeaten leaders Barcelona.
Atletico's tally of 40 points from 17 matches is a club record, overhauling the previous best of 39 set in the 1995/96 season when they last won the title.
They are through to the last 16 of the King's Cup and have a 3-0 lead over Getafe from last week's first leg and will play Russian side Rubin Kazan in the last 32 of the Europa League when the competition resumes in February.
"They [Celta] were clear about how [defensively] they were going to play and it's always tough when a game turns out that way," Adrian said in an interview with Spanish television.
"We want to carry on in the same way or even better," he added. "Everything is going well in the three competitions."
TENTATIVE REVIVAL
Valencia continued their tentative revival under new coach Ernesto Valverde when captain Roberto Soldado struck in the opening minute to set them on their way to a 4-2 home win over Getafe in the earlier kick-off.
They made heavy weather of the victory at their Mestalla stadium but held off Madrid-based Getafe reasonably comfortably in the end to climb above them into ninth.
Both have 24 points from 17 matches but Valencia have a slightly superior goal difference.
Valverde was appointed at the beginning of the month to replace Mauricio Pellegrino, sacked after the club's erratic start to the season.
Valencia have won four and lost one in all competitions since but still have a lot of work to do if they are to match the third-placed La Liga finish achieved for the past three seasons.
After Soldado's early strike, Jonas added a second for the home side in the seventh minute and Alvaro Vazquez pulled a goal back for Getafe six minutes later.
Ricardo Costa made it 3-1 on the half-hour before an Alexis header gave Getafe a sniff of hope with just over half-an-hour left that was snuffed out by a stoppage-time goal from substitute Nelson Valdez.
