Ronaldo scored his 20th La Liga goal of the season as he curled home Real's opener after just two minutes.
Athletic levelled when Javier Eraso side-footed in but James Rodriguez made it 2-1 with a long-range strike.
Toni Kroos added a third just before half-time and after Raphael Varane had been sent off, Ronaldo scored again before Gorka Elustondo's late header.
The win lifted Real above Atletico Madrid into second place in the table, although Atletico and Barcelona both play on Sunday.
Real remain unbeaten under coach Zinedine Zidane after winning their seventh successive home league game.
But it wasn't as comfortable as the score suggested in the first half as Athletic created several chances against an uncertain home defence.
Top scorer Artiz Aduriz, 35, could have had a hat-trick before the break as he headed wide, flicked an effort against the bar and saw Keylor Navas save another heading opportunity.
Real made their superior finishing count though, with Ronaldo taking his total this season to 31 goals in all competitions with the opening goal.
Rodriguez made it two goals in three games, having not previously scored in La Liga since November, while Kroos scored his first goal of the season as he turned onto a Ronaldo pass to score with a deflected shot.
Real, who play at Roma in the first leg of their Champions League last-16 tie on Wednesday, then cruised through the second half before the late flurry of activity.
Varane, who had been at fault for Athletic's first-half equaliser, received a second caution for an innocuous looking aerial challenge on Aduriz with seven minutes to go.
Ten-man Real added a fourth when Ronaldo controlled a cross from Lucas Vazquez to drill the ball home before Elustondo nodded in an Oscar de Marcos cross in the last minute to pull one back for the visitors.