Perry rallied from 6-3 down to force a decider, only to miss the brown and let the seven-time champion claim victory.
Hendry knew defeat would knock him out of the top 16 for the first time since 1988 and admitted he "got out of jail".
"If I win I might still contemplate retirement. I've a big decision to make at the end of the season," he added.
The Scot has not triumphed at the Crucible since landing his seventh title in 1999 and accepts it will become tougher to stay in the elite group.
That prospect - meaning he would have to play qualifying rounds for ranking events - has never appealed to a man who made his World Championship debut in 1986.
Hendry came through a final-frame decider in his opening match against Zhang Anda 12 months ago and it would be a similar story this time round.
The 42-year-old led 6-3 at the end of the first session but Perry made a break of 62 and then a colours clearance before levelling at 6-6.
After a superb 67 clearance allowed Hendry to lead at the mid-session interval, Perry made an 80 for 7-7 but missed the final blue in frame 15 as his opponent regained the lead.
Hawkins squeezes past Maguire (UK only)Perry rallied once more with a break of 54 and, despite a scrappy 17th going to way of Hendry, the Englishman's 69 took them to a decider.
Hendry built a lead of 53-0 before Perry hit back with a 33, yet he over-cut the final brown to a centre pocket and a period of safety ensued.
Perry gained a second opportunity but then came the crucial error as he left the brown over a corner pocket and allowed Hendry to seal the win.
"When Joe was at the table I didn't expect to get another chance," said Hendry. "His safety was different class to mine so I just had to hang in there.
"I had chances to win more comfortably, but I can take the positives out of it because I played some good stuff in the first session.
"I'm not even thinking about the rankings because I've been in danger of dropping out of the top 16 all season. I won't play in the PTC events next season so I will get punished in the rankings.
"I still love it out in the arena and my pipe and slippers are still there! It's the best place to play snooker. I'm looking forward to my next match now - I got out of jail today so I can relax now."
In Monday's earlier game, China's Ding Junhui swept into the second round with a crushing 10-2 victory over Scotland's Jamie Burnett.
The world number four held a commanding 8-1 lead overnight and completed the job with a break of 71 in the morning session.
"It feels all right, I'm playing quite well," said the 24-year-old, who has never gone past the second round before. I'm just concentrating on my game and trying to play my best."
The Masters champion crashed out in the first round of the World Championship in 2007 and has been knocked out in the second round in the three following years.
"Everybody tries hard here so the second round will be quite a difficult match to get through," added Ding, who will now face Peter Ebdon or Stuart Bingham, who finished the evening session at 4-5.
In another compelling first round match at the Crucible, Barry Hawkins survived a stirring fightback from Scotland's Stephen Maguire.
Former semi-finalist Maguire faced an uphill battle to stay in the tournament after a disappointing morning session against Hawkins who, despite being winless in his five previous visits to the Crucible, romped to a 4-0 lead.
Maguire fought back though, first to 6-3 and, then in a thrilling evening session, to 9-9.
But it proved to be in vain as Hawkins won the deciding frame to book his place in the second round for the first time.
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