The Dragons finally troubled the scorers 13 minutes from time when Jake Marketo put the finishing touches to a well-worked move and Kyle Stanley added the extras to halve the deficit.
Mitch Rein then added a second five minutes from time after Dayne Weston was penalised for putting his hands in the ball as the Panthers desperately tried to repel the fast finishing Dragons.
Ben Hornby failed with a field goal for the Dragons in the extra period, but fullback Coote made no mistake with a 25-metre effort to delight the home crowd and seal a first win in six games for the Panthers.
Dragons coach Steve Price's miserable evening was compounded by a serious looking knee injury to Michael Weyman, who was carried off after making a tackle on Josh Mansour early in the second half.
Utility Nathan Fien also limped off in the final minute of normal time leaving forcing prop Dan Hunt to fill the playmaker role in golden point.
Cleary remained tight-lipped on whether Jennings, who was named in the NSW side for next week's State of Origin opener in Melbourne, would be able to regain his place, but said he wasn't surprised Blues coach Ricky Stuart called on his services.
"I wish him all the best and hope he does well next week,'' Cleary said of his absent star.
"Ricky said that he has picked a side to score points and he certainly can do that so it didn't really surprise me.''
The former Warriors mentor also denied his decision to axe Jennings had been a wake-up call to the rest of his squad and said it was only a matter of time until they ended their wretched run of results.
"Our boys have been trying hard every week and it was going to come right at some stage,'' he said.
"We have been down on a bit of confidence and although we didn't get as much ball as we would have liked in the first half, it was probably a good thing to win that way.''
Dragons coach Steve Price admitted he was frustrated with a poor decision by Mitch Rein that led to a promising move breaking down when the visitors were chasing the win with two minutes remaining.
"We had an opportunity late in the game where we went left when the ball should have gone right,'' Price said.
Skipper Ben Hornby made his feelings known to Rein on the field in no uncertain terms but said the hooker would learn from his mistakes.
"We had all the momentum going into extra time but made a poor play in normal time and gave away a stupid penalty, but you can't play well for (only) 20 minutes and expect to win the game.''
Price also said Weyman and Fien will undergo scans on their knee injuries on Tuesday.
- AAP
