Gareth Bale made his first start in over three months and opened the scoring for Real against the second division side from the penalty spot in the 35th minute, but the hosts remained in contention until they had midfielder Pape Diamanka sent off for a second booking on the hour.
Numancia still troubled Real with 10 men and Inigo Perez gave Zinedine Zidane's side a fright by hitting the bar but Real stretched their lead with two late strikes.
Isco converted from the penalty spot in the 88th minute and Borja Mayoral scored a header in stoppage time to give Numancia a near impossible task in the second leg at the Bernabeu on Jan. 10.
"I'm happy we kept a clean sheet. We scored two goals from the penalty spot but they all count," Real defender Nacho Fernandez told reporters.
"They hit the crossbar but overall we were strong in defense and didn't suffer too much."
Triple Cup holders Barca failed to win away to Celta for the third consecutive game in all competitions and head into the second leg at the Nou Camp on Jan. 11 needing a win or a goalless draw to qualify for the quarters.
Barca forward Jose Arnaiz poked in Andre Gomes's low cross to complete a sweeping counter-attack and put Barca ahead in the 15th minute, scoring for the third Cup game in a row.
Denmark international Pione Sisto leveled for Celta in the 31st, smashing the ball into the roof of the net after Iago Aspas had hit the underside of the crossbar.
Barca's record signing Ousmane Dembele came on in the second half to make his first appearance since rupturing his hamstring in September and nearly scored the winner, but his low shot was saved by Celta goalkeeper Sergio Alvarez.
Barca hit the woodwork twice, Sergio Busquets crashing a shot against the bar and Sergio Roberto striking the post in stoppage time while Turkish international Emre Mor went close to grabbing a winner for Celta.
Coach Ernesto Valverde made seven changes to the Barca side that beat Real Madrid 3-0 in their last game while Celta, coached by former Barca assistant Juan Carlos Unzue, fielded a full-strength team.
"When a coach makes changes you always run a risk and if you lose people will say it's because you made too many but I'm happy with the squad I have," Valverde said.
"Celta pressed high and took risks, they were dangerous on the counter-attack, but so were we. In the first 20 minutes after the break we could have won the game, but we didn't take our chances. Despite that, I'm happy with our performance."
Leganes beat Villarreal 1-0 at home and Levante won 2-1 at Espanyol.
(Reporting by Richard Martin, editing by Ed Osmond)
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