Sinclair scored in either half and Luke Moore added another at the Liberty Stadium on Saturday to help the Swans' move four points clear of third-placed Cardiff in the Championship.
Steven Dobbie had already struck the post before Sinclair broke the deadlock following good link-up play with Moore.
Swansea went on to dominate the first half although they were lucky to be ahead at the break after the visitors were denied a clear-cut penalty and Davide Somma saw his header come back off the bar.
The Leeds striker was made to regret his miss when Sinclair doubled Swansea's advantage from the spot and Moore wrapped up Swansea's fourth consecutive win soon afterwards.
Although this was Leeds first defeat in eight matches, they are now without a win in three games as their charge for automatic promotion suffered a dent.
Joe Allen, Luke Moore and Dobbie came back into the starting line-up after being rested for Swansea's midweek victory at Coventry and the latter almost celebrated his return with a goal.
After making room for himself inside the area, Dobbie's effort deflected off George McCartney and came back off the post.
Swansea continued to assert their dominance so it came as no surprise when they took a 13th-minute lead.
Sinclair evaded the challenges of several defenders when cutting in from the left and after he played a clever one-two with Moore, the former Chelsea man calmly slotted past Kasper Schmeichel for his 20th goal of the season.
Nathan Dyer forced a fine save from the Leeds goalkeeper minutes later, whilst Ashley Williams headed over at the back post from Mark Gower's left-wing corner.
Despite being outclassed for the majority of the first half, Simon Grayson's men were unfortunate to go in behind at the interval.
First, they were denied a penalty when Alan Tate blatantly handled Robert Snodgrass' strike in the area.
Then Somma, who had returned to the starting line-up for the suspended Bradley Johnson in the only change to the Leeds side, saw his header tipped onto the bar by Dorus De Vries.
It proved a costly miss when Sinclair grabbed his second from the penalty spot in the 55th minute.
Dyer had just entered the area with a marauding run on the right-wing when he was felled by Max Gradel's clumsy challenge and Sinclair stepped up to send Schmeichel the wrong way.
Somma forced a magnificent save from De Vries, who tipped over the striker's shot, while at the other end, Schmeichel had to be equally imperious to prevent Gower's 25-yard free-kick finding the bottom corner of the net.
Any diminishing hopes the visitors had of picking up a point were extinguished when Moore netted Swansea's third in the 72nd minute.
The lone striker finished a good move after latching on to Dobbie's excellent through ball and dinking past Schmeichel.
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