The Australian batter contributed fully as Hyderabad scored 3-278 - the third highest in IPL history - as they beat Kolkata Knight Riders, who have also failed to make the play-offs, by 110 runs in their final match of the season.
Openers Abhishek Sharma (32 off 16) and Head put on 92 off 41 balls after Hyderabad opted to bat first.
Head scored 76 off 40 deliveries, with six sixes but if that was impressive, there was even better to come from Heinrich Klaasen, who smashed an undefeated 105 off 39 balls
Klaasen, the league's most expensive overseas player, hit nine sixes and seven fours in his second IPL century to help Hyderabad pile on a massive total. In reply, Kolkata were bowled out for 168 in 18.4 overs in Delhi.
Klaasen was promoted to No. 3 and combined with Head to add 83 off only 35 balls for the second wicket.
Klaasen got to 50 from only 17 balls. The South African then shared a partnership of 83 off six overs with Ishan Kishan (29 off 20) and reached his ton off 37 balls.
In reply, Kolkata's Sunil Narine scored 31 off 16 balls but did not get support from the top-order.
Kolkata were down to 5-70 in eight overs and the chase was pretty much done. Manish Pandey top-scored with 37 off 23 balls.
Jaydev Unadkat (3-24), Harsh Dubey (3-34) and Eshan Malinga (3-31) did the damage, though Sunrisers' Australian captain, Pat Cummins, failed to strike in his two overs.
Earlier in the day, Dewald Brevis scored 57 runs off 23 balls as bottom side Chennai Super Kings wrapped up their Indian Premier League season in style by routing first-placed Gujarat Titans by 83 runs.
Chennai won the toss and scored 5-230 in their 20 overs with Devon Conway hitting a 35-ball 52. In reply, Gujarat were dismissed for 147 in 18.3 overs.
Gujarat, Punjab Kings, Royal Challengers Bengaluru and Mumbai Indians have already secured playoff spots.
Gujarat finished with 18 points from 14 games but their spot in the top two is under threat. Second-placed Punjab (17 points) and fourth-placed Mumbai (16 points) meet on Monday in their last game, and Bengaluru (17 points) face Lucknow Super Giants on Tuesday.
Opener Ayush Mhatre gave Chennai a good start with a 17-ball 34. The big runs came from two overseas batters - New Zealander Conway providing the base, with South Africa's Brevis attacking toward the end.
Conway hit six fours and two sixes. Brevis got four fours and five sixes. Urvil Patel (37 off 19) and Ravindra Jadeja (21 not out off 18) also contributed as Chennai put up a strong total.
Gujarat's chase started badly, reduced to 3-30 in 4.3 overs, and their middle-order disappointed despite the chance to take an insurmountable points lead at the top. Sai Sudharsan top-scored with 41 off 28 balls.
Pacer Anshul Kamboj finished with 3-13, and wrist spinner Noor Ahmed 3-21. Ravindra Jadeja, who opened the bowling, took 2-17.
It was Chennai's fourth win in 14 IPL matches.
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