Yet they left a rain drenched Glyn Hopkin Stadium with a superb 4-2 win after a controversial 90 minutes.
It was quite an astonishing first half that saw five goals and, if that wasn't enough, a sending off just before the break.
It looked like it would be one-way traffic as Altrincham powered their way into a three-goal lead.
They scored with their first attempt, although the goal did come about in slightly fortuitous circumstances.
Colin Potts had a free-kick on the left touchline and his right-footed strike completely fooled Tony Roberts and ended up in the top corner.
Altrincham's second goal came just after the half-hour mark. Ged Murphy hit a terrific strike from 20 yards that left Roberts motionless.
It got even better for the Robins as two soon became three. Peter Band latched on to Colin Little's attempt in the area to score from close range.
The Daggers, however, found the perfect response by scoring twice in the last five minutes of the first half.
Paul Bruce got Dagenham off the mark with a superbly struck volley from 20 yards that arrowed into the left-hand corner.
Scott Griffiths completed the first-half scoring by firing home a Craig Mackail-Smith cross.
As the half-time whistle went the crowd had a little more action than anticipated as both teams appeared to square up.
The resulting melee left the Daggers down to 10 men as Bruce was shown a straight red card.
Both sides had chances to score in the second half. Potts missed a great chance with a header while Griffiths had an even better opportunity but shot over from barely a couple of yards.
The decisive goal was scored with 20 minutes remaining. Dagenham keeper Roberts won't look back on the goal too fondly as he spilled a Potts cross which left Little to bundle the ball into an empty net.
There was still time for a second red card for the Daggers as Shane Blackett was sent off to complete the home side's misery.