Reihana's boot was Waikato's best weapon in the early stages with three penalty goals before they broke through for their first and only try.
Tries were hard to come by with the hosts crashing over in the 13th minute, before crossing for what looked to be a decisive try in the context of the match in the 48th minute, leading to a then nine-point advantage.
Waikato's victory means they are in position for a home semifinal. Tasman's loss yesterday to Auckland not only drops the widely perceived favourites to third, but also boosts the chances of other teams taking top spot as the final sprint begins.
For Canterbury, they remain fifth with a bonus point bringing them to within one point of fourth-placed Wellington. Just two points separate third through fifth.
Meanwhile, Otago have pulled away late for a comfortable 40-22 win over Counties Manukau in Dunedin, solidifying them in second spot in the Championship.
The hosts raced out to a 21-3 lead, which was overturned early in the second half with the Steelers moving ahead 22-21 after 56 minutes.
But a surge of three tries for Otago secured a bonus-point win. They now trail Hawke's Bay on points difference.
Waikato 16 (Cortez Ratima try; Rivez Reihana con, 3 pens) Canterbury 15 (Luke Romano, Tamaiti Williams tries; Fergus Burke con, pen) HT: 6-8.
Otago 40 (Josh Timu 2, Josh Dickson 2, Freedom Vahaakolo, Charles Elton tries; Josh Ioane 5 con) Counties Manukau 22 (Alamanda Motuga, Orbyn Leger, Viliami Taulani tries; Baden Kerr 2 cons, pen) HT: 21-8.