The Tigers got off to a great start when Tansey went over the line after just three minutes, with Ellis converting.
The Rhinos responded 10 minutes later when McGuire scored and Sinfield converted before Webster grabbed a try on 16 minutes, with Ellis missing the resulting kick.
Hall claimed a try eight minutes after the restart, with Sinfield recording his second conversion of the match to give the Rhinos the lead.
However, with just six minutes remaining, Ellis atoned for his earlier miss as he converted the points to equalise for the Tigers.
He then added his third conversion to give his side the points two minutes from time.