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 who play at Real Valladolid on Saturday.
The victory also stretched their advantage over third-placed Real Madrid to seven points ahead of Real's game at Malaga, also on Saturday.
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.
"We want to carry on in the same way or even better," he added. "Everything is going well in the three competitions."
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.
Unbeaten Barca, who thumped Atletico 4-1 at the Nou Camp last weekend, can end the year with a remarkable 16 wins in 17 league matches this season if they beat Valladolid.
They will be without coach Tito Vilanova, who underwent surgery on his saliva glands on Thursday before beginning a course of chemo- and radiotherapy.
Assistant coach Jordi Roura has stepped in to take charge until Vilanova is well enough to return.
Real are looking to bounce back from last weekend's 2-2 draw at home to Espanyol and have France striker Karim Benzema back in the squad after injury.