It didn't take long for Floyd's first opportunity as he entered in the eighth inning with a two-run lead. He quickly went through the heart of San Francisco's lineup -- Matt Duffy, Brandon Belt and Hunter Pence -- with three consecutive outs to bridge the gap to closer Roberto Osuna.
"Gavin stepped up," Gibbons said. "We've been looking for a guy to do that and he did. ... He's able to get strikeouts. He has a good arm. We just have to make sure he's good and rested because he's had some arm issues in the past. He has been dominant against lefties even though he throws right-handed. He has been outstanding for us."
Storen appeared to be making progress earlier this month with three consecutive scoreless appearances but any momentum he gained was lost Sunday afternoon. Storen walked the first batter he faced and then surrendered a key double en route to a pair of earned runs in Toronto's 4-2 loss to the Dodgers.
Fellow setup man Brett Cecil, who is currently away from the team on a paternity leave, has equally struggled with an 0-5 record and a 5.59 ERA in 15 games. Gibbons gave each of his relievers an extended opportunity to keep their roles but has now decided to try something new.
Floyd's chance came Monday night but based on the early results, it certainly won't be his last.
"Today was the first time ever that I've been able to go on back-to-back days and I felt good," said Floyd, who has spent almost his entire career as a starter. "Just training your body to get into that short sample, one to two innings and get used to that. It just takes time for that to happen."
Gregor Chisholm has covered the Blue Jays for MLB.com since 2011. Follow him on Twitter @gregorMLB and Facebook, and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.