The former NRL star winger's impressive contribution took his tally to nine tries in three games and secured three successive Super League wins for Leeds.
Castleford had come into the game on the back of their first league win of the season against Huddersfield last Friday, but they fell behind at Headingley when George Brown opened the scoring with his first Super League try and Jake Connor converted.
The visitors then replied when Darnell McIntosh quickly offloaded in for another former NRL speedster, Mikaele Ravalawa, to cross in the corner, but Tom Weaver's subsequent conversion attempt flew wide.
Sivo opened his account in the 29th minute, but Connor was unable to convert and although Cameron Smith grounded just before the break, his attempt was ruled out by the video referee.
Leeds claimed a 10-4 lead at half-time and Sivo extended their advantage further early in the second half from the wing, with Connor converting.
Cas were frustrated further when stand-off Zac Cini had a try ruled out for a knock-on in the build-up and Rhinos suddenly charged ahead when Sivo scored his third of the game in the 55th minute, with Connor's kick successful.
Leeds then saw out the win to climb into second in the table, two points behind leaders Wigan, while the Tigers sit in 10th.
Leeds head coach Brad Arthur told BBC Radio Leeds: "Probably wasn't our best performance but in terms of execution I'm pretty proud of the effort and the fight and the grit that we played with.
"Those guys really took it to us, moved us around and challenged us. We looked tired a lot of the time, but we just kept hanging in there and fighting hard."
In Sunday's other match (Monday AEDT), Tyrone May pulled the strings well and Hull KR shrugged off their Las Vegas nightmare, belatedly kick-starting the defence of their Super League title with a 32-6 win at hapless Huddersfield.
Rovers were half a world away from last season's all-conquering treble-winning campaign when they crashed to a 58-6 loss to Leeds at the Allegiant Stadium last week.
And while they still seem some way from re-scaling those heights, they were effectively gifted their first points of the domestic year as Tom Davies and Mikey Lewis both crossed twice in a six-try show against the rock-bottom Giants.
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