Figueroa retired 13 of his final 14 batters. Pagan went 4 for 4 with a triple and two doubles from the leadoff spot. He also scored twice.
New York was a National League favorite back in April. But long-term injuries to Carlos Delgado, Jose Reyes, Carlos Beltran and Johan Santana decimated the roster and sent the team into a tailspin.
Many of the replacements got hurt, too, and the fourth-place Mets played mistake-filled baseball in sliding from 89-73 last year to a 70-92 record -- their worst since finishing 66-95 in 2003.
Mets players spent more than 1,480 days on the disabled list this year, more than any other major league team, according to STATS LLC.
Also beset by injuries, Houston slogged through a disappointing season as well. One game out of first place after games of July 22, the Astros then lost two of three at home to the Mets and soon fell out of the race.
Houston (74-88) finished fifth in the six-team NL Central, losing five of its final six to drop to 4-9 under interim manager Dave Clark, who took over when Cecil Cooper was fired Sept. 21.
The Mets went 41-40 in the first season at their spacious new home, Citi Field. With a crowd of 38,135 on Sunday, they drew 3,154,262 for the season.
The finale was much different than the previous two years, when the Mets completed September collapses with home losses to Florida on the final day that knocked them out of playoff contention each time.
Figueroa (3-8) snapped a five-start losing streak, though he had pitched pretty well in four of those outings. He struck out seven and walked none.
It was a nice moment for the 35-year-old journeyman, who grew up in Brooklyn rooting for the Mets. He often has plenty of family and friends in attendance at his home starts. The right-hander threw 76 of 113 pitches for strikes.
Rookie catcher Josh Thole had three hits, including an RBI single off rookie starter Wilton Lopez (0-2) in a two-run fourth. The other run scored on a throwing error by shortstop Miguel Tejada.
Luis Castillo and David Wright each hit a sacrifice fly that drove in Pagan.
Tejada doubled in the fourth to extend his hitting streak to 21 games, the longest by an Astros player since Willy Taveras set a club record with a 30-game hitting streak in 2006.
Aaron Boone played third base for Houston and went 0 for 3 in his second start since returning from open-heart surgery. The other came Sept. 2 at Wrigley Field in Chicago.
NOTES: Tejada finished one hit shy of his fourth 200-hit season. ... Wright and CF Carlos Beltran were back in the lineup for the Mets after sitting out Saturday. ... It was New York's first sweep since taking three straight at home May 25-27 against Washington. ... Astros RF Hunter Pence cut down Daniel Murphy at second base on a fourth-inning single for his league-leading 16th outfield assist. ... The Mets finished the season with a major league-low 95 homers, their fewest since hitting 93 in 1992.