The American broke twice in the first set to go in front before play was suspended due to rain. Following the delay, Samsonova jumped out to a 5-1 lead and survived a mini-comeback by Kenin to level the match.
The Russian went ahead 2-0 in the third set only to watch the fourth seed finish with a flourish, taking six of the last seven games to advance to the second round.
Kenin fights past Samsonova, rain to move on
Kenin got an immediate break, stinging a backhand winner to take the lead and dug out of a 0-30 hole to consolidate her advantage for a 2-0 edge. A forehand error brought up break point for Samsonova and the Russian converted with a backhand winner to level the set at 2-2.
At 4-4, Kenin had another chance to break and duly took it when the Russian missed a backhand wide. Serving for the set, she battled through a tough game and took the lead when Samsonova sent a forehand long.
Following an almost two-hour rain delay, Samsonova came out the quicker of the two players, holding and then breaking the Kenin serve when the American double-faulted on break point to hand the Russian a 2-0 lead.
A marathon fifth game saw Samsonova come through to hold after Kenin sliced a backhand into the net as the Russian jumped out to a 4-1 lead. She broke to love, blasting a crosscourt backhand for a winner to claim a 5-1 advantage.
Kenin hit back, breaking and holding to put the pressure back on the Russian. With a second chance to close out the set, Samsonova fired a forehand winner to set up double set point and another shot from that wing forced a weak reply from Kenin to level the match at one set all.
She kept up her fine play to start the third set, breaking Kenin in the first game with a forehand winner before the American struck back, a backhand winner levelling the set at 2-2. Both players held until the eighth game when the fourth seed broke for a 5-3 lead.
Serving for the match, Kenin arrived at 40-30 and when Samsonova fired a final backhand wide, the Australian Open champion escaped with a hard-earned victory.