The defending champions have won only one of their first four games and sit in a very unfamiliar 12th place after last weekend's 1-0 defeat by Sevilla.
Boss Jose Mourinho was highly critical of his players before the match against City on Tuesday, accusing them of lacking hunger and commitment in all but their Spanish Supercopa victory over Barcelona.
But he was much happier after watching Madrid come from behind in the final moments to claim a 3-2 victory over City and will be looking for more of the same when they travel to neighbouring Rayo Vallecano on Sunday.
Mourinho said: "We played well against Barcelona at home. We won the Supercopa by leaving everything out on the field.
"You can lose matches playing like that. Not like we did in Seville and Getafe. Now all I worry about is the here and now. A team like Real Madrid cannot say that we won the cup and that we are no longer interested in winning in the league.
"Real Madrid wants to win the historic 10th (European Cup) and we will fight for it. We have to go for all of the titles that we can.
"We'll end up with them all or just with the Supercopa, but you have to give everything in every match. Football is great when you leave everything on the field."
Rayo have had a good start to the season and go into the match three points ahead of their opponents, who could have defender Sergio Ramos back in the starting line-up after Raphael Varane was surprisingly given the nod against City.
Madrid are already eight points behind their great rivals Barcelona, who have had no such worries, winning their first four matches to top the table.
Barca also had to come from behind to claim a 3-2 Champions League victory over Spartak Moscow yesterday, though, and manager Tito Vilanova welcomed the challenge.
He said: "I would have preferred to have won more easily and suffered less. However, I think these types of games are good for all of us. Football is not easy. The comeback proves that this team is eager to win."
Barcelona will look to make it five out of five in the league at home to Granada on Sunday, but they will be without both their first-choice centre-backs.
Carles Puyol was already sidelined and Gerard Pique limped out of yesterday's game early on with a foot injury, but full-back Jordi Alba could return after illness.
Second-placed Malaga marked their Champions League debut with an impressive 3-0 victory over Zenit St Petersburg in midweek and they travel to Athletic Bilbao on Sunday.
Real Mallorca have also made a strong start and they host Valencia on Sunday while fourth-placed Sevilla visit Deportivo La Coruna the following day.
Osasuna and Espanyol prop up the table with a point apiece and both are on the road this weekend, with Osasuna travelling to Real Zaragoza and Espanyol visiting Real Betis.
In other matches, Celta Vigo host Getafe, Levante face Real Sociedad and fifth-placed Atletico Madrid meet Real Valladolid.
Saturday's La Liga Fixtures
Sunday's La Liga Fixtures
Monday's La Liga Fixtures