Josh Wilson took two penalties for the Bucks - scoring one in the 36th minute, and missing one in the 48th - and John-Paul Kissock also got his first goal for the club late on.
Mark Shelton, Craig Westcarr - via the spot - and Paul Marshall struck for the Reds, who just survived a spell of Telford pressure at the end to claim an important three points.
Telford only won three of 22 National League North away games in 2016 - and one of those was a 3-2 success at the Impact Arena in March.
They opted for a flexible 4-3-3 formation in attempt to play between the lines. Elliot Hodge and Dave Hibbert came into the side, while there was a place on the bench for 16-year-old youth prospect Jordan Broome.
It was a kamikaze first half which involved two penalties being awarded, and converted, and the Bucks backline looked particularly fragile.
Rob Smith's charges started off at a pedestrian pace and were made to pay as Alfreton took the lead after quarter of an hour. Dave Hibbert went down and appealed for a foul on the halfway line - but nothing was given by referee Anthony Tankard.
The Reds capitalised on a lapse in concentration as Shelton escaped the attention of Ben Bailey and squeezed the ball under James Montgomery. Hibbert then picked up a booking for dissent.
Another sloppy piece of defending should have ended in Telford levelling the scores in the 24th minute, but Hodge took one touch too many and could only shoot straight at Reds goalkeeper Ross Etheridge in a one-on-one situation.
Chaos reigned as both sides scored from the spot within the space of two minutes. Firstly, the hosts were awarded a spot-kick in the 34th minute after Wilson clipped Marshall in the area and Westcarr - in similar fashion to his goal at the New Bucks Head on Boxing Day - coolly sent Montgomery the wrong way.
The Bucks then made an almost immediate response as Wilson atoned for his error by smashing the ball in from 12 yards out, after Kissock was pushed to the ground.
Just as Telford looked to be growing in confidence and perhaps capable of forcing an equaliser, the hosts's two-goal lead was restored.
Kallam Mantack's hopeful low cross from the right somehow made its way to Marshall on the opposite flank, and he fired the ball into the far corner with his left foot in the 43rd minute.
You sense Smith would have given his charges a stern talking-to at the break, and a change was made for the second period as Connor McCarthy replaced Hibbert.
They made a flying start to the second half and, after McCarthy had a one-on-one was saved, were given another penalty.
Bradley Reid, who initially seemed to have wasted a good opportunity, was brought down by the hands of Etheridge. Wilson stepped up to the spot again, and once more opted for power, but had head-in-hands as his effort struck the post and flew wide.
After a much quieter 15-minute period, the Bucks decided to shift to a 4-4-2 system as Paul McCone came on for Ben O'Hanlon in the 64th minute - McCone filling at right-back and Dwayne Samuels moving to left-back.
After Ben Bailey was booked, their third and final change came in the 73rd minute as Danny Reynolds entered the fray in place of Hodge, who was one of Telford's busiest players.
Despite the substitutions, Telford struggled to create many problems for the Alfreton defence. The home side missed a couple of good opportunities to score before Kissock saw his deflected strike hit the net in the 89th minute.
Luca Havern and Reynolds both had big chances to equalise and Ben Bailey was sent-off for a second bookable offence, but Alfreton held on for the victory.
Alfreton (4-5-1): Etheridge; Gascoigne, Jordan, McGowan, Heaton; Mantack, Marshall, Monkhouse (c), Shelton, Wilson; Westcarr (Hearn, 87). Subs not used: Clayton, Spiess, Nyoni, Priestley.
Telford (4-3-3): Montgomery; Samuels, Havern (c), Bailey, O'Hanlon (McCone, 64); Rea, Kissock, Wilson; Hodge (Reynolds, 73), Hibbert (McCarthy, 45), Reid. Subs not used: Broome, Cowan.
Referee: Anthony Tankard
Attendance: 601

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