23‑Nov‑1981 | Johannesburg | Hard | R16 | 58 | 14 | (1)Vitas Gerulaitis [USA] d. Moor | 6-3 6-3 | | | | | | | | | |
23‑Nov‑1981 | Johannesburg | Hard | R32 | 58 | 96 | Moor d. Nick Saviano [USA] | 7-6 6-2 | | | | | | | | | |
2‑Nov‑1981 | Hong Kong | Hard | R32 | 53 | | Lloyd Bourne [USA] d. Moor | 2-6 6-3 6-4 | | | | | | | | | |
26‑Oct‑1981 | Tokyo Indoor | Carpet | R32 | 54 | 43 | Chris Lewis Nzl [NZL] d. Moor | 6-4 7-5 | | | | | | | | | |
19‑Oct‑1981 | Tokyo Outdoor | Clay | QF | 54 | 9 | (1)Eliot Teltscher [USA] d. (8)Moor | 6-1 6-4 | | | | | | | | | |
19‑Oct‑1981 | Tokyo Outdoor | Clay | R16 | 54 | | (8)Moor d. (14)Larry Stefanki [USA] | 7-5 6-4 | | | | | | | | | |
19‑Oct‑1981 | Tokyo Outdoor | Clay | R32 | 54 | | (8)Moor d. Bob Weise W055 [USA] | 6-3 6-4 | | | | | | | | | |
19‑Oct‑1981 | Tokyo Outdoor | Clay | R64 | 54 | | (8)Moor d. Yoshiya Hamano [JPN] | 6-1 6-2 | | | | | | | | | |
21‑Sep‑1981 | San Francisco | Carpet | R16 | 56 | 1 | (1)John Mcenroe [USA] d. Moor | 6-3 6-2 | | | | | | | | | |
21‑Sep‑1981 | San Francisco | Carpet | R32 | 56 | 60 | Moor d. Phil Dent [AUS] | 6-4 6-3 | | | | | | | | | |
1‑Sep‑1981 | US Open | Hard | R128 | 49 | 17 | (15)Vitas Gerulaitis [USA] d. Moor | 4-6 6-3 6-0 3-6 6-2 | | | | | | | | | |
17‑Aug‑1981 | Atlanta | Hard | QF | 42 | 9 | (1)Eliot Teltscher [USA] d. (5)Moor | 6-1 6-3 | | | | | | | | | |
17‑Aug‑1981 | Atlanta | Hard | R16 | 42 | | (5)Moor d. John Hayes [USA] | 6-3 1-6 6-2 | | | | | | | | | |
17‑Aug‑1981 | Atlanta | Hard | R32 | 42 | | (5)Moor d. Marty Davis [USA] | 6-3 1-6 6-2 | | | | | | | | | |
3‑Aug‑1981 | Indianapolis | Clay | R64 | 41 | | Hans Simonsson [SWE] d. (11)Moor | 6-2 6-4 | | | | | | | | | |
28‑Jul‑1981 | North Conway | Clay | R64 | 34 | | Fernando Dalla Fontana [ARG] d. (15)Moor | 6-4 3-6 6-3 | | | | | | | | | |
20‑Jul‑1981 | Washington | Clay | R16 | 37 | | Stanislav Birner [CZE] d. (14)Moor | 6-4 2-6 7-6 | | | | | | | | | |
20‑Jul‑1981 | Washington | Clay | R32 | 37 | | (14)Moor d. Craig Wittus [USA] | 6-2 6-2 | | | | | | | | | |
20‑Jul‑1981 | Washington | Clay | R64 | 37 | | (14)Moor d. Ron Hightower [USA] | 3-6 6-3 6-0 | | | | | | | | | |
13‑Jul‑1981 | Boston | Clay | R64 | 33 | | Bernard Fritz [FRA] d. (8)Moor | 7-6 6-1 | | | | | | | | | |
25‑May‑1981 | Roland Garros | Clay | R16 | 37 | 1 | (1)Bjorn Borg [SWE] d. Moor | 6-0 6-0 6-1 | | | | | | | | | |
25‑May‑1981 | Roland Garros | Clay | R32 | 37 | 67 | Moor d. Ilie Nastase [ROU] | 6-3 6-2 6-1 | | | | | | | | | |
25‑May‑1981 | Roland Garros | Clay | R64 | 37 | 44 | Moor d. Jose Luis Damiani [URU] | 6-3 7-6 6-1 | | | | | | | | | |
25‑May‑1981 | Roland Garros | Clay | R128 | 37 | | Moor d. Anders Jarryd [SWE] | 6-2 6-4 6-2 | | | | | | | | | |
18‑May‑1981 | Rome | Clay | R64 | 37 | 8 | (3)Jose Luis Clerc [ARG] d. Moor | 7-5 6-1 | | | | | | | | | |
11‑May‑1981 | Hamburg | Clay | R64 | 37 | 73 | Mark Edmondson [AUS] d. Moor | 2-6 6-2 6-3 | | | | | | | | | |
20‑Apr‑1981 | Las Vegas | Hard | R16 | 37 | 6 | (1)Ivan Lendl [USA] d. Moor | 7-5 3-6 6-3 | | | | | | | | | |
20‑Apr‑1981 | Las Vegas | Hard | R32 | 37 | 57 | Moor d. Tim Gullikson [USA] | 6-3 2-6 6-1 | | | | | | | | | |
13‑Apr‑1981 | Los Angeles | Hard | R16 | 38 | 72 | Nick Saviano [USA] d. (7)Moor | 6-1 6-3 | | | | | | | | | |
13‑Apr‑1981 | Los Angeles | Hard | R32 | 38 | 54 | (7)Moor d. Butch Walts [USA] | 6-1 7-5 | | | | | | | | | |
6‑Apr‑1981 | Houston | Clay | R16 | 37 | 70 | Sammy Giammalva Jr [USA] d. Moor | 6-4 7-5 | | | | | | | | | |
6‑Apr‑1981 | Houston | Clay | R32 | 37 | 16 | Moor d. (4)Johan Kriek [USA] | 6-3 6-4 | | | | | | | | | |
23‑Mar‑1981 | Napa | Hard | R16 | 36 | | Tim Mayotte [USA] d. (2)Moor | 7-5 4-6 6-1 | | | | | | | | | |
23‑Mar‑1981 | Napa | Hard | R32 | 36 | | (2)Moor d. Colin Dibley [AUS] | 6-4 6-4 | | | | | | | | | |
9‑Mar‑1981 | Tampa | Hard | R32 | 35 | | Sammy Giammalva Jr [USA] d. (3)Moor | 6-0 4-6 6-2 | | | | | | | | | |
2‑Mar‑1981 | Denver | Carpet | QF | 35 | 32 | (4)Mel Purcell [USA] d. (5)Moor | 7-5 6-3 | | | | | | | | | |
2‑Mar‑1981 | Denver | Carpet | R16 | 35 | 81 | (5)Moor d. Nick Saviano [USA] | 3-6 6-3 7-6 | | | | | | | | | |
2‑Mar‑1981 | Denver | Carpet | R32 | 35 | | (5)Moor d. Robert Vant Hof [USA] | 6-4 7-6 | | | | | | | | | |
23‑Feb‑1981 | Memphis | Carpet | QF | 36 | 67 | Tom Gullikson [USA] d. Moor | 6-4 6-1 | | | | | | | | | |
23‑Feb‑1981 | Memphis | Carpet | R16 | 36 | | Moor d. Jeff Borowiak [USA] | 6-2 3-6 6-3 | | | | | | | | | |
23‑Feb‑1981 | Memphis | Carpet | R32 | 36 | | Moor d. Ricardo Acuna [CHI] | 6-4 7-6 | | | | | | | | | |
23‑Feb‑1981 | Memphis | Carpet | R64 | 36 | 23 | Moor d. (11)John Sadri [USA] | 6-7 6-4 6-2 | | | | | | | | | |
16‑Feb‑1981 | La Quinta | Hard | R16 | 40 | 3 | (1)Jimmy Connors [USA] d. Moor | 6-0 6-2 | | | | | | | | | |
16‑Feb‑1981 | La Quinta | Hard | R32 | 40 | 28 | Moor d. (15)Jose Higueras [ESP] | 6-3 6-1 | | | | | | | | | |
16‑Feb‑1981 | La Quinta | Hard | R64 | 40 | 81 | Moor d. Tim Wilkison [USA] | 6-4 6-2 | | | | | | | | | |
2‑Feb‑1981 | Richmond WCT | Carpet | SF | 47 | 6 | (2)Ivan Lendl [USA] d. Moor | 4-6 6-3 7-6 | | | | | | | | | |
2‑Feb‑1981 | Richmond WCT | Carpet | QF | 47 | 36 | Moor d. Raul Ramirez [MEX] | 7-5 6-3 | | | | | | | | | |
2‑Feb‑1981 | Richmond WCT | Carpet | R16 | 47 | 27 | Moor d. Tomas Smid [CZE] | 6-3 6-3 | | | | | | | | | |
2‑Feb‑1981 | Richmond WCT | Carpet | R32 | 47 | 7 | Moor d. (3)Harold Solomon [USA] | 6-4 7-5 | | | | | | | | | |
26‑Jan‑1981 | Philadelphia | Carpet | R32 | 50 | 21 | (14)Yannick Noah [FRA] d. Moor | 6-4 3-6 6-3 | | | | | | | | | |
19‑Jan‑1981 | Monterrey WCT | Carpet | R32 | 51 | 9 | (2)Vitas Gerulaitis [USA] d. Moor | 6-2 6-4 | | | | | | | | | |