Combining CMOS and TTL logic
You are exactly right. And any resistor value less than about 10k will work fine, as long as it is more than about 330 ohms (Look at the data sheet for the maximum current into a low output, Iol(max). Assume 15 mA. Then a low output will nominally put 5 volts across the resistor, and R = V/I = 5/.015 = 333.) 

2.2 k is a perfectly good value. If you're doing this a lot, you can consider using somewhat higher values to reduce the power wasted in the resistors.