The former Livingston captain opened the scoring in the eighth minute with a close-range header before Anthony McDonald grabbed his first goal for the club 14 minutes later.
Against a side three rungs further down the SPFL ladder, Hearts dominated proceedings, although the only complaint from the Hearts supporters was that the margin of victory should have been considerably bigger.
Woeful finishing, married with a series of outstanding saves from on-loan Hibs goalkeeper Kevin Dabrowski, ensured the away team had to remain vigilant for the entire 90 minutes.
Dabrowski even earned a round of applause from the away fans when it was announced over the Tannoy that he was the man of the match.
It was a return to familiar ground for Hearts manager Levein, 38 years after beginning his football career at Central Park, and 22 years on from his first managerial posting at Cowdenbeath.
The trademark stock car track encompassing the pitch remains, as does the terracing on three sides of the ground.
Something Levein may not have expected, though, was a playing surface that appeared in pristine condition.
The visitors made no fewer than six changes, four days after beating Dundee United on penalties in their opening Group A encounter.
Alongside Halkett, fringe players Bobby Burns, Oliver Bozanic, Dario Zanatta and Steven MacLean were also handed starting jerseys.
A noticeable absentee was Harry Cochrane, following on from the midfielder’s omission on Friday evening at Tynecastle.
Backed by a large travelling support, the visitors meant business from the first whistle.
Less than 25 seconds were on the clock when Zanatta forced Dabrowski into a save from close range.
The opportunities kept coming; MacLean headed over when he should have scored before Halkett was also wasteful with a similar effort.
Defender Halkett, however, made no mistake when he got on the end of Bozanic’s corner in the eighth minute – powering a header past Dabrowski.
Cowdenbeath have been on the end of heavy defeats to Hearts in recent years, losing 5-0 in the League Cup last season and 10-0 and in the Championship in 2015.
The early signs were it could be another bruising tussle for the part-timers.
But just like against United, Hearts were again guilty of squandering clear-cut openings.
Conor Washington found himself through on goal but had his effort repelled by Dabrowski before McDonald lifted a half volley just wide.
Hearts finally created the two-goal cushion their play warranted in the 22nd minute, McDonald placing a MacLean cross into the net from six yards as the visitors’ insatiable desire for goals showed no sign of abating.
Perhaps motivated by the fact he is employed by Hearts’ arch rivals, Dabrowski again frustrated the Edinburgh club before the half was out, Washington and Dario Zanatta failing to find a way past the home goalkeeper.
There was a feeling of deja vu at the start of the second half; Hearts creating a clear goalscoring opportunity and the keeper coming to the rescue.
Zanatta had a free run at Dabrowski on the break from McDonald’s pass but again the Pole came out on top in the duel.
Hearts looked to the bench for inspiration as Uche Ikpeazu replaced Washington on the hour mark.
The replacement came at a time when the hosts were beginning to enjoy more territorial possession, with Hearts goalkeeper Zdenek Zlamal at least being called upon to deal with some crosses.
Before the game finished there was still time for Dabrowski to further demonstrate his expertise in goal, this time getting down to Aidan Keena’s low drive.