Eighth-seed Clijsters comfortably saw off the dangerous Croatian Karolina Sprem 6-3 6-2, with the US Open champion continuing to look comfortable in her first Wimbledon appearance since 2006.
The former world number one will next face Russian 27th seed Maria Kirilenko, who beat Shenay Perry, with a possible encounter against compatriot Henin to follow.
Clijsters, whose best Wimbledon achievement is reaching the last four, said: “The score was a lot easier than it was to play. I had to work extremely hard but I was consistent and that was the most important thing.”
Henin, whose last outing at SW19 before her retirement was in 2007, was made to sweat before overcoming Kristina Barrois.
Five-times champion Venus Williams started in imperious form against shock Eastbourne champion Ekaterina Makarova on Centre Court before recovering from a scare.
Williams served powerfully and made few errors as she won the first set 6-0 in just 25 minutes and looked to be on course for a convincing victory before failing to serve out for the match. However, the American broke back immediately to secure a 6-0 6-4 triumph.
There was a surprise on Court Five with Israel’s Shahar Peer, the 13th seed, losing to Angelique Kerber 3-6 6-3 6-4.