Paul Hartley, Jan Vennegoor of Hesselink and Shunsuke Nakamura all left the club in the summer.
There was little initial reward for the home side other than a long-range free-kick from Shunsuke Nakamura as Hearts settled.
Shunsuke Nakamura worked a good one-two with Miller before his powerful strike was deflected over by the outstretched leg of Ehiogu.
Shunsuke Nakamura's free-kick to the front post was headed on by Scott McDonald and Caldwell powered the ball home from 12 yards.
Shunsuke Nakamura flighted the ball into a busy six-yard box and the big Dutchman rose highest to flick the ball past Zaluska.
Shunsuke Nakamura, Scott Brown and Paul Hartley or Barry Robson need to keep possession whilst looking to play that incisive ball into the box.
Maloney broke the deadlock after 29 minutes when he collected a superb pass from Shunsuke Nakamura to fire home past Inverness goalkeeper Ryan Esson.
They responded in kind, Van Persie finding himself hooking a dangerous cross from substitute Shunsuke Nakamura over his own crossbar from within the six-yard box.
Hearts' Marius Zaliukas and Celtic's Shunsuke Nakamura had efforts saved in the second half and late pressure from the visitors failed to yield a winner.
The favour was repaid by United in the 21st minute when Loovens rose free to glance Shunsuke Nakamura's front-post corner past Lukasz Zaluska and put Celtic 1-0 ahead.
Five minutes from the interval Shunsuke Nakamura's first-time pass sent Samaras clear and the Greek striker slid his angled, low drive past Combe but also past the far post.
Celtic had sent on substitutes of their own, with Paul Hartley and Shaun Maloney replacing Barry Robson and Shunsuke Nakamura - but they were having trouble creating any clear-cut opportunities.
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