Hoffenheim scored a goal in each half to keep struggling Arminia Bielefeld in deep trouble at the foot of the Bundesliga.
Wellington opened the scoring after 25 minutes following an error by Bielefeld defender Andre Mijatovic.
Things went from bad to worse for Mijatovic after the break as he was sent off after 81 minutes for a second yellow received for hauling down Demba Ba in the box.
Sejad Salihovic stepped up to convert the resulting penalty to put the result beyond any doubt.
The loss means Bielefeld remain 16th in the standings, inside the drop zone but still just a point from safety with two games remaining.
Bielefeld started well and hit woodwork twice in the early exchanges.
Oliver Kirch volleyed Christopher Katongo's cross against the left upright from 12 yards after four minutes while Mijatovic headed a free-kick from Thorben Marx against the right post a short time later.
In between, Boubacar Sanogo almost put the visitors in the lead but his close-range header whistled past the right post.
Bielefeld's Robert Tesche had a goal disallowed for offside after 11 minutes before he set up Katango 10 minutes later. The Zambia striker was denied by Timo Hildebrand, who was set for a solid night between the posts.
The hosts fell behind against the run of play when a mistake by Mijatovic allowed Wellington a free effort on goal which he duly dispatched beyond Dennis Eilhoff.
Bielefeld almost pulled one back four minutes later but Radim Kucera failed to find a way past Hildebrand from six yards out.
The game petered into a midfield battle until after the break when Artur Wichniarek went close for the hosts from a free-kick.
Eilhoff kept his side in the match when he denied Chinedu Obasi but Robert Tesche could not capitalise moments later as wasted Bielefeld's best chance of the half, Hildebrand parrying his effort from the edge of the box.
Mijatovic came close with a header a minute later but he failed to convert as the hosts' final chance went begging.
The defender's miserable night then took another turn for the worse when he floored Ba in the area to pick up the red card, after which Salihovic held his nerve to double Hoffenheim's lead and seal the points.