Afinogenov will miss six weeks after breaking his left wrist and Novotny is out indefinitely after aggravating a left ankle injury.
"It's going to make things a lot tougher. We're going to have to dig in," coach Lindy Ruff said. "You've got to grind your way through it."
Afinogenov was hurt late in the second period, when he fell and landed awkwardly. And yet he returned for one more shift to score his 23th goal, tying the game at 1 by converting a Thomas Vanek's rebound. Tests taken during the second intermission revealed the break.
Novotny, meanwhile, was hurt with seven minutes left when he twisted his ankle while checking Matt Greene into the end boards. The injuries come a week after Buffalo lost forward Paul Gaustad (torn tendon), who is out for the season, and defenseman Jaroslav Spacek (broken left hand). Spacek is expected to miss about month.
Ruff was otherwise impressed by the resilience Buffalo showed, rallying from a 1-0 deficit to win its fourth straight -- all decided by one goal -- and sixth in seven games.
"I thought it was a gutsy effort," Ruff said.
Briere scored on a 2-on-1 break and at the end of a long shift. Getting a pass from Jochen Hecht inside the Oilers zone, Briere patiently waited for defender Toby Petersen to slide past him. Then, stepping into the middle, Briere lifted a shot beating Dwayne Roloson over the right shoulder.
"It's one of those times of year where we're getting hit now, it's our turn," Briere said of the injuries. "But you can't stop and worry too much about it. There's guys that are going to come up and it's their chance to step up."
Shawn Horcoff scored for Edmonton, which is 0-1-1 in opening a critical seven-game road trip as it attempts to climb back into playoff contention. The defending Western Conference champions at least earned a point to inch within six of the eighth and final playoff spot.
"We can't dwell on losing the one point," said Roloson. "We have to use this is a building block."
Roloson was the difference in keeping the Oilers in. He stopped 29 shots, including nine in the opening 5 minutes of the second period.
Besides getting a glove out to snag Ales Kotalik's one-timer from the right circle, Roloson -- with help from defenseman Ladislav Smid -- denied Daniel Paille on a wraparound attempt following a scramble in front.
The Oilers' offensive road woes, however, continued. They've managed a league-low 55 goals away from Edmonton.
"We had all kinds of chances to get things to go really right for ourselves. But where we've put ourselves is not good enough," Oilers coach Craig MacTavish said.
Ryan Miller made 27 saves as Buffalo won its sixth straight home game, the team's longest streak since winning seven straight early into the 1999-2000 season. The Sabres also snapped a six-game home winless streak (0-4-2) against Edmonton, Buffalo's last win a 4-1 decision on Oct. 18, 1995.
Miller's only miscue came when Horcoff threaded a snap shot from the left circle that glanced in off the goalie's glove seven minutes into the game.
- Oilers RW Fernando Pisani (concussion) missed his second straight game while C Jarret Stoll (concussion) missed his sixth straight. Neither is currently traveling with the team.
- Vanek extended his point streak to four games, in which he has four goals and an assist.
- Afinogenov's goal was Buffalo's first at home against Edmonton in 178 minutes and 16 seconds, dating to Geoff Sanderson's third-period goal in a 2-2 tie on Feb. 13, 2000.