I use this site:
In the "flight number" box, type in the IATA number of the airline, followed by the flight number. Note the Number must be 4 characters. For example, for Delta flight number 123 you'd type in DL0123. Use the 0 as a placeholder.
Then below select "Last 7 days" instead of "today only" and below that select "HTML table" instead of "ACARS Style Output". Then hit enter.
Then it will give you a list of flights, just look for the one with the correct date. Also note flights late at night, maybe 11pm might register as taking place "tomorrow". The time listed doesn't always match up to takeoff time.
This site works for about 60% of flights. For some reason some airlines and some flights don't show up... It should list flights once they're in the air, there's no delay.