First, Ronaldo broke his own mark of last season by scoring in the 3-1 come-from-behind victory over Sporting Gijon.
Later Saturday, Messi grabbed a brace as Barcelona also hit back from a goal down to defeat Levante 2-1 as the champions stayed four points behind Real with the mouthwatering, season-defining El Clasico to come next weekend.
On a night of landmarks, Real’s third goal was their 107th of La Liga this season.
It puts them level with John Toshack’s Real Madrid team of the 1989-90 season with Jose Mourinho’s side still with five matches to play.
“The records come as a result of the work of all the players who have given so much and deserve to be champions,” said Real assistant coach Aitor Karanka.
“For those who say that Jose Mourinho is a defensive coach then you just need to look at these statistics.”
A Sergio Ramos handball had seen Miguel Angel De las Cuevas put Sporting ahead from the penalty spot after half an hour before Gonzalo Higuain equalised with a header after 36 minutes.
Ronaldo finally broke Sporting’s resistance with a header after 73 minutes and, following the dismissal of Roberto Canella for a second yellow card, Karim Benzema hit the third.
Nuri Sahin began in midfield for Real alongside Sami Khedira, with Xabi Alonso suspended.
Jose Callejon was included in a four-pronged attack with Benzema on the bench, with Mourinho holding him back for the Champions League semi-final with Bayern Munich on Tuesday.
Sporting won a controversial penalty after Ramos slid in to clear the ball and the referee claimed he handled. De las Cuevas sent the ball straight down the middle of the goal to give Sporting the lead.
Real responded with Khedira going close with a shot from the edge of the area before Higuain headed in the equaliser.
Ramos crossed for the Argentine, who had not been picked up by Sporting defence, and he knocked the ball past keeper Juan Pablo.
Mourinho brought on Benzema and Angel Di Maria for the second half.
Ronaldo had further shots from distance and Benzema missed a half chance but they appeared to be lacking inspiration before Ronaldo headed in a 74th-minute Di Maria cross.
Canella, who was already on a yellow card, picked up a second for a foul on Di Maria and then, nine minutes from the end, Benzema sealed the win with a shot from a Mesut Ozil pass.
Levante went ahead against Barcelona from a 23rd-minute penalty converted by Jose Barkero.
But Messi then hit a second half brace with his second goal, from the penalty spot after a foul by Pedro Botelho on Juan Cuenca, drawing him level with his great Portuguese rival Ronaldo on 41 league goals.
“This result is important in lifting us for the upcoming match in London and then the Madrid game,” said Barca coach Pep Guardiola with his side facing Chelsea in the Champions League semi-final on Wednesday.
“Now we are going to think about the Chelsea match and then Madrid which will be a very hard game. We have won the last three titles but if they win this time then that will be that.”
Barcelona had a depleted defence with Dani Alves and Gerard Pique only fit for a place on the bench along with Andres Iniesta who was rested.
Pedro Rodriguez had a shot saved by Levante keeper Gustavo Munua and Thiago Alcantara headed wide as Barca looked comfortable in possession.
Levante set their stall to defend deeply and try and find the pace and strength of frontman Arouna Kone on the counter.
It was a policy which paid dividends as they took the lead against the run of play from the penalty spot after a handball from Busquets.
Keeper Victor Valdes was unable to hold a corner and Busquets blocked a header from Juanfran Garcia with his hand. The referee awarded a penalty which was converted clinically by Barkero.
Barca’s cause was starting to look increasingly forlorn when Messi drew them level from the edge of the area on 64 minutes.
Then, following a foul by Pedro Botelho on Juan Cuenca, Messi won the game for Barcelona from the penalty spot with 18 minutes left.