Andy Murray failed to capitalise on a one-set lead against top seed Ivan Ljubicic as he bowed out of the Zagreb Indoors tournament in the first round.
Henman (right) fared better than his fellow Briton
The 18-year-old Briton took the first set 6-4 against his Croat opponent only for Ljubicic to claim the second 6-2.
Despite holding break point in game one of the third set, Murray was unable to convert and eventually lost it 6-3.
But Tim Henman fared better in his second-round match, beating third seed Richard Gasquet 6-4 6-4.
It was his second successive win since bowing out of the Australian Open in the first round last month.
The British number one broke serve in the opening game of the match and then consolidated to seize a 2-0 lead before moving to 5-3.
Gasquet battled to 5-4 but Henman served out for the set with the minimum of fuss.
The Frenchman dropped serve in the third game of set two, struck back for 2-2 but Henman quickly broke again to lead 4-3 before completing a hard-fought win.
"I played really solid," said Henman. "I served very, very well in the first set and gave him few chances and, obviously, breaking him in the first game was a good start and gave me a confidence booster.
"It's a good win. He's a top-20 player and I've beaten him twice this year. Hopefully I can keep building on this."
Henman's next opponent could be 17-year-old French Open junior champion Marin Cilic, of Croatia, who faces Italian Andreas Seppi.
Earlier in the day, Croatian Ivo Karlovic dismissed German Rainer Schuettler in straight sets to set the stage for a second-round showdown against compatriot Mario Ancic.
Other winners included Spanish eighth seed Feliciano Lopez, who eventually edged past Sweden's Robin Soderling 7-6 4-6 6-1, while Russia's Mikhail Youzhny overcame Czech Tomas Zib 6-4 3-6 6-1.
In the first of Wednesday's second-round matches Switzerland's Stanislas Wawrinka, who stunned second seed David Ferrer in his first match, lost 6-4 6-4 to Austria's Stefan Koubek.