Britain had already qualified one team for the Olympics with driver John Jackson having secured a spot.
With hopes resting on Deen's shoulders, the team brought in the rest of Jackson's four-man crew from GBR sled 1 for Sunday's competition in Austria as they looked for the points needed for him to climb into the top 20.
And the trio of Stuart Benson, Joel Fearon and Bruce Tasker delivered alongside Deen recording an overall time of 1:42.71minutes from their two runs to finish comfortably inside the top 15.
Jackson, partnered by John Baines, Ben Simons and former GB sprinter Craig Pickering finished in 20th while the overall victory went to the Latvian team driven by Oskars Melbardis.
Steven Holcomb, currently third in the overall World Cup standings, guided his American side to second with Thomas Florschuetz and Germany in third.
Meanwhile in the women's two-man event, Britain's Paula Walker gave one last push to ensure she is on the team to Sochi as she and new partner Sarah Adams finished 14th.
It was the first time the pair had competed together on the World Cup stage and they finished in a time of 1:47.88minutes, 1.60seconds behind eventual winners Jamie Greubel and Lauryn Williams of the USA.
Selection for the Great Britain team is announced on Wednesday with Walker, 11th in the two-man bobsleigh in Vancouver 2010, currently sitting 13th overall in the rankings.
"Eight years of hard work has gone into this," she said afterwards. "Vancouver was a bonus, so I hope this is enough [for Sochi]."