In a game dominated by the wind, Kyle - on loan from Coventry City - struck early on and the home defence held on as Brighton staged a revival with the wind at their backs in the second half.
After scoring 15 goals in their previous four home games, it made a change for Hartlepool to win by a single goal, but they'll be delighted with the points from a tight game.
With the strong wind behind them in the first half, it was no surprise that Hartlepool took command early on, and they were in front on 12 minutes.
Joel Porter's neat ball from the left of the area gave James Brown a chance right in front of goal, but Brighton keeper Michels Kuipers made a brilliant save to turn the ball round his left-hand post.
The corner was taken short and when Brown swung the ball over to the far post, Kyle rose high to loop his header over Kuipers and into the net.
Little was seen of the Brighton attack, and when they did break out on-loan Robbie Savage screwed his shot yards wide after a right-wing pull-back from Joe Anyinsah.
But Brighton did well to hold out until the break, though they had some luck when Porter's header was cleared off the line in the dying seconds.
The wind caused problems for both teams in the second half, though Anyinsah hit the home bar from 20 yards on 62 minutes, and at the end of a great home move a few minutes later Richie Jones was only inches away from doubling Hartlepool's lead.