Tasman equalised in the 13th minute when No 8 Sione Talitui scored following a powerful scrum and clever support play from the visitors. First five-eighth Mitchell Hunt added the extras.
The hosts took the lead for the second time when No 8 Devan Flanders scored in the 22nd minute after bursting off the back of a five metre scrum. Falcon again slotted the conversion.
Magpies openside flanker Brendon O'Connor did well to force the scrum with a superb kick and chase move.
The Magpies lost lock Geoff Cridge to a yellow card for a high tackle in the 26th minute on Mako second five-eighth Alex Nankivell. Four minutes later, Mako winger Leicester Faingaanuku scored a soft try which Hunt converted to tie the score again.
Those were the only points conceded before Cridge's return. However, the Mako took a 19-14 lead into the halftime break after Faingaanuku's brother and fellow winger Lotima Faingaanuku scored a minute into injury time.
The Magpies defence on this occasion was as soft as the visitors defence was when Mikaele-Tu'u opened the scoring. However, with 40 per cent of the territory and 40 per cent of the possession in the first half the Magpies were competing well with the unbeaten Premiership leaders.
Tasman's ability to keep the ball alive at confrontation time led to Leicester Faingaanuku's second try in the 43rd minute which Hunt converted from out wide. The visitors had earlier constructed some quality phase play when the Magpies failed to secure the kick off.
Hawke's Bay managed to keep the Mako out for nine minutes before Hunt scored after more accurate support play from the visitors. Hunt again converted.
Four minutes later, Mako second five-eighth Alex Nankivell scored and Hunt added the extras. Just three more minutes had ticked over before Mako substitute hooker Hugh Roach burst away to score and captain and fullback David Havili converted to put the visitors ahead 47-14.
To their credit, the Magpies didn't throw the towel in and were rewarded with a try to winger and former Mako Caleb Makene in the 67th minute after good work from the Magpies best player on the day Flanders. Falcon again converted.
Substitute prop Jason Long scored the Magpies' final try in the 77th minute after some quality support play. Falcon converted to end the scoring.
Match highlights
Heartstopper: Mako captain and fullback David Havili's 10th minute tackle on his Magpies counterpart Tiaan Falcon. It was a beauty but fortunately no damage was done to Falcon.
Turning point: Mako winger Leicester Faingaanuku's second try in the 43rd minute which first five-eighth Mitchell Hunt converted to give the visitors a 26-14 lead. The Magpies were never going to recover from this deficit against a quality side like the Mako.
Player of the match: Mako second five-eighth Alex Nankivell. Powerful on the carry with 90 run metres. A rock on defence. Only just ahead of winger Leicester Fainggnuku and No 8 Sione Talitui.
Scorers: Tasman Mako 47 (Sione Talitui, Leicester Faingaanuku 2, Lotima Faingaanuku, Mitchell Hunt, Alex Nankivell, Hugh Roach tries; Mitchell Hunt 5 cons), Hawke's Bay Magpies 28 (Marino Mikaele-Tu'u, Devan Flanders, Caleb Makene, Jason Long tries; Tiaan Falcon 4 cons). HT: 19-14.