Because Canyonlands National Park has a north and a south entrance separated by over 80 miles, there are two routes you can drive to reach Zion National Park.
Canyonlands North Route (Island in the Sky District): Follow Route 113 from the park to Route 191. Turn left (away from Moab) and travel north to Interstate 70. From here follow I-70 all the way until it merges with I-15. Head south on I-15 and take Exit 27, about 30 miles south of Cedar City. Turn left on Route 17 and follow into Route 9 which will lead you directly into Zion.
The drive, especially for Interstate travel, is above-average for scenery. I-70 winds up and over the San Rafael Swell and through Fishlake National Forest.
Canyonlands South Route (Needles District): Follow Route 211 out of the park and to Route 191. Turn right and travel south. At Bluff 191 merges with Route 163. Stay on 163 and follow it through one of the world's most photographed western settings, Monument Valley. From here 163 crosses into Arizona. At Kayenta, 24 miles from the state line, turn right (west) onto Route 160 and follow for 42 miles before turning right onto Route 98. This snakes into Page, home to the Glen Canyon Dam. From Page follow Route 89 back into Utah and through the Escalante National Monument. Turn left on Route 9 at Mount Carmel Junction and follow into Zion.