The former Middlesbrough youngster pounced to net in the 29th and 34th minutes as the Lions were ripped apart.
But it was midfielder Marc Bridge-Wilkinson who ran the show, setting-up two goals and grabbing one himself on the stroke of half-time.
Bridge-Wilkinson chipped a 15th-minute free-kick into the Millwall area and teenage hitman Joe Garner rose unmarked to power a six-yard header past the stranded Rab Douglas for the opener.
Carlisle should have had a second when Peter Murphy's defence-splitting ball sent Garner clear, but his pull back was just too far for stretching strike partner Graham with the goal gaping.
The Lions almost hit back in the 24th minute as Dave Brammer hit the woodwork with a curling effort with the outside of his right boot from 25 yards.
But Bridge-Wilkinson cleverly played in Graham and he slipped a low shot into the corner of the net for number two.
He grabbed his second when Joe Anyinsah drilled over a low cross that Graham tucked away from six yards.
It got worse for the Lions in the 37th minute when Richard Shaw was stretchered off.
Bridge-Wilkinson completed the rout on the stroke of half-time when he stepped up to curl a brilliant free-kick over the wall and into the top corner from 20 yards.
Graham came close to completing hit hat-trick in the second period but had his head in his hands as he lashed a low shot just wide and then saw a looping header bounce onto the roof of the net.