While working on Mystery Capablanca Letter, I downloaded all of the games played between Capablanca and Alekhine to see if there were any openings similar to the mystery game. Of the 49 games I found three where the first two moves for both sides matched, but that was it.
As long as I had the games in hand I decided to calculate the overall score between the two players. The results are shown below.
I found it curious that Capablanca lost three games with White during the 1927 Alekhine - Capablanca Title Match: the 1st, 11th, and 21st games. That happened to equal the margin of loss (+6-3=25).
That link leads to my page on the match that says, 'Before the match, the score between the two opponents was +4-1=5 in favor of Capablanca', although the table shows +5-0-7. Ahem! I'd better change that page pronto.