Seven years later, he was with the Houston Oilers when they staged the biggest collapse in playoff history, ultimately losing to the Buffalo Bills in overtime, 41-38.
One year after that, still with the Oilers, his team failed to hold a 10-point lead against Joe Montana and the Kansas City Chiefs, and fell, 28-20.
"Personally, I'm getting tired of it," Jones said of his string of stunning defeats. "This stuff [simply getting to the playoffs] is way overrated.
"I want to go to the Super Bowl."
It would seem to be Jones' best chance, if not his last, in a distinguished career of chasing NFL quarterbacks.
Reaching the Super Bowl is the one accomplishment that has escaped him. He has been selected to the Pro Bowl. He ranks eighth all-time in career sacks with 113. He has played in more than 200 NFL games.
But the closest he has gotten to the Super Bowl was last season, when the Packers came up a quarter short.
This week, when asked what the Super Bowl means to him, Jones wound the tape of his playoff past and talked about failure.
"Next to God and family, it means everything," he said. "Those are the three most important things in my life. Depending on what day of the week it is, the order changes.
"I've been in the league 13 years. I've been to the playoffs 11 times. I've been to the championship game. I've been through the Buffalo fiasco. I've lost to Kansas City when Joe Montana came back to beat us. I was on the Raiders team that lost to New England -- one of the worst teams that ever played [in the playoffs]."
Jones' postseason history is remarkable both for its depth and its defeats. He has played in 16 postseason games over 13 years, and won only five of them. In 10 years with the Raiders and Oilers, he won only two of 10 playoff games.
The losses took their toll on Jones and his teams. He called the Raiders' loss to New England the most defining because it signaled the end of an era. They had held home-field advantage in the AFC playoffs in 1985 before self-destructing with six turnovers against the Patriots.
It took the Raiders five years to get back to the playoffs, and when they made it again in 1990, they were humiliated by the Bills in the AFC title game, 51-3.
In the 10 years since the Raiders lost to the Patriots, they've made the playoffs only three times.
"I look at the New England game as the turning point for the Los Angeles-Oakland Raiders," Jones said. "They haven't played good football since that point."
Jones was traded to Houston in 1988, where he endured six postseason defeats. If the Raiders' loss was the most defining, the 1992 loss in Buffalo, where the Oilers blew a 32-point lead, was the most frustrating.
"Anyone could see that coming, the way the organization was treating players," he said.
When the Oilers lost to the Chiefs in the postseason the next year, another era ended. Houston hasn't been back to the playoffs since.
Jones left Houston as a free agent after that to join the up-and-coming Packers and All-Pro defensive end Reggie White.
"It couldn't have been money because I had better offers from Houston and Atlanta," Jones said. "I did not want to play for a losing team.
"I've never had delusions about myself as a player. I've played with [defensive linemen] Howie Long, Bill Pickell, Lyle Alzado, William Fuller, Ray Childress. You see the trend?
"I can't do this by myself. I wanted to find a team that had great players around me. Reggie was here. John Jurkovic and Bryce Paup were here then, too. I'm not Michael Jordan, but I make a helluva Scottie Pippen."
He makes a pretty good businessman, too. He owns a financial services company and a sports apparel business in Beverly Hills, Calif., where he lives in the off-season. Football, he said, is a diversion from real life.
"It's insane out there in the business world," Jones said. "This is easy. Roll out of bed, hit a couple of people and you get paid."
But it's not the money that motivates Jones at this point in his career; it's his pursuit of a Super Bowl ring.
"I have another goal, for my company to be ranked in Fortune 500," he said.
"That's how we're judged. Not by money, but by success. It's not the money. There are a whole bunch of rich guys out there without rings."
NFC championship game
Carolina Panthers (13-4)
at Green Bay Packers (14-3)
Time: 12: 30 p.m. Sunday
TV: Chs. 45, 5
Line: Packers by 12
AFC championship game
Jacksonville Jaguars (11-7)
at New England Patriots (12-5)
Time: 4 p.m. Sunday
TV: Chs. 11, 4
Line: Patriots by 7 1/2
Sean Jones file
Position: Defensive end
G ... Tk .. Ast. .. Sacks .. FF .. FR
15 .. 29 .... 6 .... 5.0 .... 2 ... 1
G ..... Tk .. Ast. .. Sacks .. FF .. FR
201 .. 394 .. 207 ... 113.0 .. 11 .. 13
Highlights: One of the NFL's most consistent pass rushers. His five sacks this season are his lowest since his rookie year (1984). Has had double digits in sacks five times, registering a career-high and AFC-leading 15.5 in 1986 with the Los Angeles Raiders. Has 24.5 sacks in three seasons with the Packers. Ranks eighth all-time with 113 career sacks.
Team ...... Sea. .. Playoff loss
Raiders ... 1985 .. 27-20 to Patriots
Skinny: Raiders gave up 20 points on six turnovers
Oilers .... 1992 .. 41-38 to Bills
Skinny: Oilers led 35-3 before collapsing
Oilers .... 1993 .. 28-20 to Chiefs
Skinny: Joe Montana led Chiefs' comeback
Packers ... 1995 .. 38-27 to Cowboys
Skinny: Packers led 27-23 in fourth quarter
Pub Date: 1/08/97