Barry Robson scored a brilliant late winner as Middlesbrough kept up the pressure on leaders Southampton.
Scott McDonald was twice thwarted by keeper Frank Rost and Barry Robson and Georgios Samaras wasted decent chances.
The Catalan club prepared for last season with a similar trip and on that occasion Henry's eye was caught by Barry Robson.
Barry Robson's surging run after 20 minutes forced a corner for the visitors, but Paul Hartley's cross evaded Caldwell at the back post.
Some strong defending from Barnsley kept the home attack at bay, with Jason Shackell blocking shots from Barry Robson and then Andrew Taylor.
Caley Thistle started the second half more sprightly and almost equalised when Barry Robson's corner was met at the near post by Paul Ritchie.
Shunsuke Nakamura, Scott Brown and Paul Hartley or Barry Robson need to keep possession whilst looking to play that incisive ball into the box.
But the Teessiders looked most likely towards the end with Ruddy saving brilliantly from Barry Robson and Kris Boyd and Hoyte also going close.
Scott Brown, Barry Robson and Paul Hartley hounded Carrick and Fletcher incessantly and for the greater part, held on to the ball when they could.
Striker Chris Killen and midfielders Barry Robson and Willo Flood have all moved to Boro on permanent deals and defender Stephen McManus has joined them on loan.
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.
"Tony will be happy with the result against Hapoel - there's a lot of positives to take from the overall performance, " said Collins after the victory following goals from Georgios Samaras and Barry Robson.
Celtic's speed and movement was a delight to watch, but Rangers' doggedness was denying them threats on goal until a fine Hinkel cross was met by the head of Barry Robson and looped from 15 yards off the face of the crossbar.
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