The Rams rallied from behind three times, then benefited from an overturned pass-interference penalty in the waning seconds to beat Detroit 41-34.
The victory spoiled the return of Lions offensive coordinator Mike Martz, who was head coach in St. Louis for six seasons.
Detroit (0-4) built a 34-33 lead before the Rams (3-1) got the ball with 4:42 to play at their own 44. Seven plays later, on third down at the 5, Bulger threw to the right side and Isaac Bruce wriggled into the end zone for his first touchdown of the season with 1:56 to play.
Bulger and Bruce then connected on a 2-point conversion.
"One game you're kicking six field goals, another game you're scoring points," Linehan said. "The bottom line is you've got to feel good when you win in this league."
Detroit drove to the St. Louis 37, then appeared to get a break when Rams rookie Ty Hill was called for interference against Az-Zahir Hakim in the end zone with 22 seconds left. But after a huddle, the officials reversed the call because the ball was tipped, and Kitna's fourth-down pass sailed out of the end zone.
The Rams have been much more conservative in their first season under Linehan than they were under Martz, whose teams generally scored a lot, but gave up a lot, too. Though they've cut down on turnovers with only three lost fumbles and no interceptions this season, St. Louis had only two touchdowns and had not topped 18 points in their first three games.
Bulger was 26-for-42 for 328 yards and three touchdowns. Torry Holt had six catches for 102 yards and a touchdown and Bruce caught seven passes for 100 yards and a score.
Detroit has made steady progress on offense under Martz. After scoring 13 points in their first two games, the Lions have scored 58 in their past two.
"We weren't good enough on defense. It comes down to three turnovers they get and we get zero. That's the game in a nutshell."
Martz was not made available to the media following the game.
Kitna was 29-for-43 for 280 yards, two touchdowns and two interceptions.
Mike Furrey and Kevin Jones scored two touchdowns each for the Lions. Furrey, a former Ram, caught two touchdown passes from Kitna in the second quarter. Jones rushed for 93 yards on 19 carries, including 35- and 7-yard scoring runs in the second half.
Roy Williams caught nine passes for 139 yards, his second successive game with over 100 yards receiving.
The Rams went into halftime down 17-16, then retook the lead on their first drive of the second half, with Bulger connecting with Holt on a 16-yard touchdown pass.
A 65-yard kickoff return by Eddie Drummond set up a 20-yard field goal by Jason Hanson, and Detroit went up 27-23 with 4:23 to go in the third quarter when Jones converted a third-and-1 run into a 35-yard score.
The Rams rallied again, aided by a 48-yard pass-interference foul on Jamar Fletcher that gave St. Louis a first-and-goal at the 5. Stephen Jackson's 1-yard touchdown run made it 30-27. Jackson ran for 81 yards on 22 carries.
Detroit responded with a 10-play, 71-yard drive that ended with Jones' 7-yard run on a draw play with 11:11 to play.
Wilkins' fourth field goal, a 47-yarder, cut the margin to 34-33 with 6:16 to play.
The Lions announced that their game Oct. 8 at Minnesota will be moved to Monday night, Oct. 9, if the American League Divisional Series between Minnesota and Oakland goes to a fifth game, which would be played next Sunday. ... RamsPro Bowl left tackle Orlando Pace, still feeling the effects of a concussion suffered in Week 2 in San Francisco, was inactive. Todd Steussie replaced Pace at tackle and Adam Goldberg replaced Steussie at left guard.