Madrid now have seven points from their opening three games after a bright start to the season, while the reported potential signing of Kylian Mbappe could give them another boost before the end of the transfer window on Tuesday.
Ancelotti, who returned to the club after the resignation of Zinedine Zidane, has seen some of his tougher decisions pay off so far, with Gareth Bale and Isco impressing after being brought back into the fold.
Los Blancos will not play their first home match of the season until September 11 due to the ongoing renovation of the Santiago Bernabeu.
But they still lead the way in LaLiga ahead of Sevilla and Valencia on goals scored.
Betis remain winless after opening the season with two draws following a feisty encounter at the Benito Villamarin which saw the hosts have five players and veteran coach Manuel Pellegrini booked.
Both teams looked dangerous early on, with Betis goalkeeper Rui Silva making a good save from Madrid defender Eder Militao in the seventh minute.
Shortly afterwards, away 'keeper Thibaut Courtois had to get down smartly to keep out Nabil Fekir's well-struck effort from long range.
Karim Benzema thought he had put the capital giants ahead in the 53rd minute but saw his effort ruled out for offside.
But the visitors did break the deadlock just after the hour mark through the unlikely source of Carvajal.
Vinicius Junior did well to keep the ball in play before right-back Carvajal volleyed home Benzema's cross.
Madrid centre-back David Alaba almost gifted Betis an immediate equaliser as he attempted to cut out a cross, but sent the ball spinning just past his own post.
Eden Hazard dropped to the bench, came on as a late substitute as the away side closed out an ultimately comfortable win.