A brace from Amari Morgan-Smith moved 10-man Luton up to third in the table at the expense of Telford.
Morgan-Smith converted Robbie Willmott's left-wing cross for the first and clinically rifled home a second from 18 yards.
Sean Newton's effort, blocked by Dean Beckwith, was Telford's best chance.
The home side struggled to break down Luton even after defender Ed Asafu-Adjaye fouled Phil Trainer and was sent off for two bookable offences.
VIEWS FROM THE DRESSING ROOM
AFC Telford United manager Andy Sinton told BBC Radio Shropshire:
"I'm disappointed with the two goals we gave away. First one they're telling me was offside.
"The second goal at any level of football, if you give the ball away from your own kick-off it's criminal.
"We showed them too much respect in the first half, second half was better but we were chasing the game."
Luton Town manager Gary Brabin told BBC Three Counties Radio:
"The sending off's put us under a bit of pressure, but I said to the lads I'm not only proud we've won two games and kept clean sheets back-to-back, I think we've showed character.
"It is hard when you're down to 10 men.
"We showed a really good, spirited performance and I thought we defended fantastically."
AFC Telford: Young, Salmon (Farrell 85), Whitehead, Killock, Newton, Samuels, Davies (Brown 46), Trainer, Rodgers (Adams 69), Mills, Sharp.
Subs Not Used: Robinson, Valentine.
Booked: Samuels, Mills, Killock.
Luton: Tyler, Asafu-Adjaye, Antwi, Beckwith, Howells, Morgan-Smith, Keane, Lawless, Fleetwood (O'Connor 82), Crow (Dance 71), Willmott (Watkins 90).
Subs Not Used: Kevin Pilkington, Kissock.
Sent Off: Asafu-Adjaye (67).
Booked: Asafu-Adjaye, Keane, Morgan-Smith.
Goals: Morgan-Smith 8,46.
Ref: Kevin Johnson (Somerset).