The Leeds skipper then kicked over two penalties before a drop goal gave his side a 11-0 advantage at the break.
The hosts got themselves in front on the hour when Richards intercepted a pass before running the length of the pitch to score his side's second try of the match. He then successfully made the conversion to put Wigan 12-11 in front.
Leeds went on the offensive in what was a tense final 10 minutes and they were rewarded for their persistence when Sinfield kicked over with two minutes to play.
Brett Finch lined up a drop goal in the final seconds that would have levelled the scores, but he missed the posts as Leeds held on for the win.