James Phillips' late try gave Exeter Chiefs victory over Newport Gwent Dragons in a tight Challenge Cup encounter at Rodney Parade.
The number eight drove from the base of a five-metre scrum to break Welsh resistance and go level on points at the top of Pool 4 with Perpignan.
Phillips' number eight rival Toby Faletau started and ended a length of the field try to give Dragons the lead.
But Exeter hooker Simon Alcott barged over to begin the Exeter fight-back.
Jason Tovey, back in the Dragons' starting line-up, booted the hosts into the lead after just six minutes and exchanged further penalties with Exeter fly-half Ignacio Mieres as the Welsh region edged into a 9-6 lead after 24 minutes.
With Exeter's Alcott in the sin-bin, the Dragons surged into a commanding lead thanks to Faletau.
The Wales World Cup star picked up a spilled Exeter pass and burst through the Chiefs' defence from his own 22.
Faletau had fly-half Tovey and wing Aled Brew in support and the three produced a neat interchange of passes to send the number eight crashing over.
Tovey added the conversion and kept the scoreboard ticking over to hand the hosts a 10-point advantage at the break.
But the Chiefs came storming back and made the perfect start to the second half when Alcott crashed over on 51 minutes from a close-range ruck.
Steenson continued to chip away with penalties and Chiefs snatched the victory at the death when Phillips picked up from the base of a five-metre scrum and dived over following a dominant final quarter.
Newport Gwent Dragons: Martyn Thomas; Tonderai Chavhanga, Adam Hughes, Anitelea Tuilagi, Aled Brew; Jason Tovey, Wayne Evans; Nathan Williams, Lloyd Burns, Nathan Buck, Adam Jones, Rob Sidoli, Danny Lydiate, Gavin Thomas (capt), Toby Faletau.
Replacements: Rhys Buckley for Burns (65), Phil Price N. Williams (66), Keiron Jenkins for Buck (66), Lewis Evans, Tom Brown, Joe Bedford, Lewis Robling, Will Harries for Brew (57).
Exeter: Arscott; Sestaret, Shoemark, Dollman, Jess; Mieres, Phibbs; Sturgess, Alcott, Mitchell, Hayes, Bentley, White, Scaysbrook, Phillips.
Replacements: Steenson for Mieres (41), Barrett for Phibbs (48), Tui for Sturgess (59), Clark for Alcott (59), Andress for Mitchell (59), Muldowney for Bentley (59), Ewers for White (12). Not Used: Tatupu.
Sin Bin: Alcott (20).
Referee: Matieu Raynal (France).