It’s been a slow, steady climb for CBS’ Emmy winner “The Amazing Race,” but its hit status was cemented Tuesday night when it wrapped its seventh edition with series-best scores.

After claiming its second consecutive Emmy trophy last fall, the globetrotting unscripted skein gradually built upon its solid-but-unspectacular ratings during its winter and spring editions to become one of the anchors of the Eye’s strong weekly lineup.

In its finale Tuesday, “Race 7” built throughout its two hours, placing second to Fox drama “House” from 9 to 10 and then crossing the finish line with a dominant victory in primetime’s final hour. Fox still won the night with “American Idol” and “House,” but CBS enjoyed its strongest Tuesday in key demos since November 2001.

According to nationals from Nielsen, “Amazing Race” averaged a 6.8 rating/17 share in adults 18-49 and 16.01 million viewers overall, peaking with a 7.6/20 in the demo in its final half-hour, when it beat NBC and ABC combined. This is the best delivery for any edition of “Race,” which ends the season as the No. 5 reality show on television, having surpassed the fading “Fear Factor” on NBC and “The Bachelor” on ABC.

Tuesday’s finale saw married couple Uchenna and Joyce of Houston edge out lovebirds Rob and Amber of “Survivor” fame. Popularity — and notoriety — of the latter couple, whose wedding will be aired by CBS in primetime May 24, is credited by some for boosting viewership of “Race.”

Elsewhere, Fox combo of “American Idol” (10.2/29 in 18-49, 24.73m) and “House” (7.4/18, 18.80m) rolled from 8 to 10, lifting the net to its 17th straight Tuesday victory. “House” retained a best-yet 73% of its lead-in.

The WB’s “Gilmore Girls” had another strong outing at 8 (2.3/7 in 18-49, 5.39m), placing second to “Idol” in adults 18-34 (2.6/8). And the season finale of “Veronica Mars” on UPN (1.2/3 in 18-49, 2.99m) didn’t see much of a ratings bump although it did deliver the show’s best women 18-34 score since November (2.1/5).