Eichel had a goal and an assist to help the Sabres beat the Lightning 4-1 on Tuesday night.
The Sabres had lost seven in a row against the Lightning dating to last season. Buffalo captured the final game of the season series after it was outscored 10-3 in three earlier losses to Tampa Bay.
"I thought it was a big game for our team, it's the 10th of November, but I still thought to beat the Lightning at this point of the season is a big game for us," Sabres coach Dan Bylsma said.
Johnson made a full-out diving save across the crease to take a goal away from Nikita Kucherov in the second.
Buffalo (7-8-0) has won four of five for the first time since December 2014.
Steven Stamkos scored his eighth goal this season for the Lightning, who have lost seven of nine (2-6-1). The defending Eastern Conference champions, the NHL's top-scoring team last season, have 12 goals over the last nine games.
"It's tough ... they're trying," Lightning coach Jon Cooper said. "They're not going in."
Tampa Bay (7-8-2) is 2-4-0 at home after posting a home record of 32-8-1 last season.
Eichel opened the scoring 5:57 into the first by beating Andrei Vasilevskiy, who had lost his stick, from the left circle during a power play. It was his first NHL road goal and sixth overall.
"It's great to beat them and build some confidence off that game," Eichel said.
After Stamkos got a power-play goal 52 seconds into the second, Franson made it 2-1 at 1:40 with his first goal in 18 games off a pass from Eichel.
"I liked the response after we gave up the goal," Bylsma said. "We come up with a big push, a big play by Jack."
Vasilevskiy lost his stick twice during the second, but the Sabres were unable to capitalize.
Foligno stopped a 17-game goal drought at 5:24 of the third when his soft wrist shot from the top of the left circle eluded Vasilevskiy.
Ristolainen added an empty-net goal in the final minute.
Tampa Bay outshot the Sabres 31-27. The Lightning were 1 for 5 on the power play, while Buffalo converted 1 of 3 chances.
"There's no sense in getting frustrated," Stamkos said. "The only guys that are going to get us out of this is ourselves."
Buffalo is 28-15-3 at Tampa Bay for its best road record against any opponent.
NOTES: Lightning RW Ryan Callahan, who normally plays on the line with Stamkos, has no assists in his last 15 games. ... Tampa Bay LW Ondrej Palat, hurt Saturday at Minnesota, is wearing a brace around his left ankle and will miss three to five weeks. ... Eichel has two goals and five points during a three-game point streak. ... Eichel drew a second-period hooking penalty in front of the Lightning net after a nifty rush that started in the Sabres' defensive zone. ... Buffalo D Carlos Colaiacovo returned after missing two games with an upper body injury. ... Sabres D Mike Weber didn't play due to a lower body injury.