After winning each of its last six games by at least 20 points, Memphis (18-0, 5-0 Conference USA) didn't take a double-digit lead until Douglas-Roberts' two-handed jam with 6:21 remaining made it 48-38.
Rose set up the dunk by tipping away Calvin Walls' pass and then tracking it down in the frontcourt before firing a pass to Douglas-Roberts.
Shawn Taggart followed with a 3-pointer, only his sixth 3 in 11 attempts this season, and Douglas-Roberts added a layup off a baseline inbounds pass as Memphis reeled off nine straight points to go up 54-38 with 4:02 left.
The last time Memphis reached No. 1, Virginia Tech was waiting hours later to pull off a 64-56 upset on Jan. 10, 1983. It took the school just over a quarter-century to get back to the top.
Taggart, a reserve who'd played only 10 minutes in the Tigers' two previous games, ended up with 14 points for his third-highest total of the season and Joey Dorsey had a career-high 19 rebounds.
Calvin Walls led the Golden Hurricane (9-7, 1-3) with 12 points.
The Tigers' inside tandem of Dorsey and Robert Dozier was neutralized much of the night by 7-footer Jerome Jordan, and the Tigers couldn't get much going from outside.
Memphis shot only 37.9 percent, its third-lowest mark of the season, and was 4-for-16 from 3-point range but was able to make up for it by holding the Golden Hurricane to their season-low in scoring and only 22 percent shooting in the second half.
Tulsa drew its first sellout crowd in over two years, and the first capacity crowd at the Reynolds Center for an opponent other than Oklahoma since sixth-ranked Gonzaga visited in February 2004.
The Golden Hurricane fell behind 12-4 early after three straight baskets by Douglas-Roberts but were able to stay in it by locking down on defense and holding Memphis to only 35 percent shooting in the first half.
Sam Mitchell's putback got Tulsa within 28-24 at halftime, but the Golden Hurricane missed six of their first seven shots in the second half and missed their chance to put real pressure on the Tigers.
Memphis has won 28 straight Conference USA games.