Matt Bryant kicked four field goals, and Atlanta's coverage units recovered two fumbles to help send the sixth-seeded Falcons to the divisional round, where they will face the top-seeded Philadelphia Eagles on Saturday.
"This game was kind of the way our season was, we had to grind it out," Ryan said. "It doesn't matter where we're going, we're going. It doesn't matter. Keep it going is our main goal."
The Rams were shaky at times in their first playoff game since 2005. Quarterback Jared Goff got off to a slow start, and Pharoh Cooper and Blake Countess lost fumbles on kick returns, leading to 10 first-half points for Atlanta.
The Falcons benefited from the Rams' miscues on special teams to take an early 13-0 lead.
Los Angeles responded with a Goff touchdown pass to Cooper Kupp and a 35-yard field goal from Sam Ficken to cut the deficit to 13-10 at halftime.
The Falcons opened the second half with two time-consuming drives that resulted in Bryant field goals, including a 54-yarder that gave Atlanta a 19-10 lead heading into the fourth quarter.
Ryan capped an eight-play, 83-yard drive with an 8-yard touchdown pass to Jones that put Atlanta in front 26-13 midway through the fourth quarter.
Ryan finished 21 of 30 for 218 yards. Jones had nine catches for 94 yards.
With Los Angeles down by 13, Goff led the Rams back down the field but couldn't complete the drive and turned the ball over on downs at the Atlanta 5-yard line.
"We knew it was going to take all four quarters," Falcons linebacker Deion Jones said.
Goff finished 24 of 45 for 259 yards. Todd Gurley had 101 yards rushing, and Robert Woods caught nine passes for 142 yards for the Rams.
Devonta Freeman scored on a 3-yard touchdown run in the second quarter and led the Falcons' ground game with 66 yards. Behind Freeman and Tevin Coleman on the ground, Atlanta had a 15-minute advantage in time of possession.
Atlanta reached last year's Super Bowl before losing to the New England Patriots. The Falcons have been up and down this season, but they advanced to the next round, where they'll get a crack at the Eagles, who are playing with backup quarterback Nick Foles.
Only two No. 6 seeds have won the Super Bowl, the 2005 Pittsburgh Steelers and the 2010 Green Bay Packers.
--Field Level Media
Atlanta | L.A. Rams | |
Devonta Freeman | Player | Todd Gurley |
18 | Attempts | 14 |
66 | Yards | 101 |
3.7 | Avg Yards | 7.2 |
1 | Touchdowns | 0 |
22 | Long | 33 |
Atlanta | L.A. Rams | |
Julio Jones | Player | Robert Woods |
9 | Receptions | 9 |
94 | Yards | 142 |
10.4 | Avg Yards | 15.8 |
1 | Touchdowns | 0 |
27 | Long | 38 |
Yards | Scoring | Defense | ||||||
Team | Tot | Rus | Pas | TD | FG | INT | Sck | FF |
Atlanta | 322 | 124 | 198 | 2 | 4 | 0 | 3.0 | 1 |
L.A. Rams | 361 | 115 | 246 | 1 | 2 | 0 | 3.0 | 0 |