Karim Benzema scored twice in the second half at Estadio Alfredo Di Stefano, lifting Madrid to a fourth straight victory in all competitions.
Zinedine Zidane's men joined Real Sociedad and Atletico Madrid on 26 points atop the table, but they struggled for large parts at home to Athletic.
Madrid played more than 75 minutes against 10 men following Raul Garcia's red card, but Toni Kroos' fine opener was cancelled out by Ander Capa.
But Benzema haunted Athletic once more to continue Madrid's winning run.
Athletic had made a decent start before Garcia's aggression proved costly, the midfielder's third foul inside 13 minutes – this one on Kroos – leading to his second yellow card.
Madrid struggled to create much of note despite their numerical advantage, although they improved late in the half as Vinicius Junior drew a good save from Unai Simon from close range and Federico Valverde poked wide.
The opener arrived on the stroke of half-time through Kroos, who produced a superb first-time finish from 20 yards after a Vinicius pass.
Athletic responded and made the dream start to the second half thanks to Capa.
Starting a run in his own half, Capa exchanged passes with Oscar de Marcos before keeping his composure to tuck away an equaliser after his initial effort was parried by Thibaut Courtois.
Athletic had done superbly to keep a lacklustre Madrid, who lacked ideas, at bay until Benzema struck in the 74th minute.
Dani Carvajal delivered a wonderful cross, Benzema getting on the end of it to head in his fifth LaLiga goal of the season.
Athletic went close to a stunning late equaliser, but Courtois stepped up with a huge stop to deny Mikel Vesga, with Madrid going down the other end and Benzema sealing the points after a pass from Luka Modric.
Madrid momentum keeps building
Madrid were under huge pressure to begin the month, facing Champions League elimination and struggling in LaLiga. Now, they have moved level on points with the leaders in the league, having already reached the last 16 in Europe's top club competition. With momentum building after a fourth straight win, silverware again looks in reach for Zidane and his men.
Benzema steps up again against Athletic
Kroos had dominated the encounter with Madrid playing against 10 men, but they still needed Benzema to step up late. The striker's header means he has been involved in 18 goals (13 goals and five assists) in 22 league games against Athletic, his joint-most against any opponent in LaLiga.
