The Scot, the 2012 winner at nearby Zhailjau Golf Club, went into the second round at Nurtau Golf Club one adrift of the overnight lead after an opening 67.
The 30-year-old followed yesterday’s blemish-free score by making two birdies and dropping no shots over the front nine, reaching the turn in 34.
After his first two bogeys of the week at holes 11 and 13, Henry teed it up on the par-3 16th knowing he needed to find something special to claw his way back up the leaderboard.
What came after was just that, with Henry following up birdie by making the first albatross of his career at the par-5 17th – by holing out from 212 yards with a 6-iron.
He then went on to roll in a 14-foot birdie putt at the last – meaning he signed for a second consecutive 67.
Henry trails Sweden’s Mikael Lundberg and Argentina’s Estanislao Goya after reaching 10 under par overall, and the European Challenge Tour winner admitted his late flurry changed what was otherwise a difficult day in Almaty.
“It was amazing how quickly it changed from being a frustrating day to one I was absolutely delighted with,” said the Clydebank man.
“Up until that point I had played really well but had not been able to get the ball in the hole. I had a little bit of a disaster on the 13th – I had a four-footer for birdie but ended up walking away with a bogey – so I was a little bit disgruntled with that.
“I then went on to play really well in the build up to the last three holes. On 16 I put it to about five feet and then went on to hole the putt for birdie.
“On 17 I hit a really great drive and then hit a six iron and just managed to chase it in between the bunkers.
“This course is about as firm as concrete so it just bumped on and I was able to watch it run on into the hole. It was a bonus during a day which until that point had been quite frustrating.
“I had never had an albatross before and I almost felt a little bit cheeky birdieing the last after it. Overall it was an amazing turnaround.
“Obviously winning here before means I always enjoy coming back. Although I did win on a different course, I definitely think there is something about Kazakhstan for me.”
Four other Scots made the cut in the Challenge Tour major, including Grant Forrest after he backed up his opening 67 with a 71 to sit joint-20th on six-under.
Jamie McLeary (68-72) is two shots futher back, with Bradley Neil (67) and Jack Doherty (71) both on three-under.
Neil, who is sitting ninth in this season’s Road to Oman, bounced back from an opening 74 by carding an eagle and four birdies.