The Kings lead 17-10 at the half-time interval.
Falcons flyhalf Juan Kotze opened the scoring with a penalty before his opposite number Ntabeni Dukisa drew the scores level at 3-3.
Just under ten minutes later the Kings were awarded a penalty and then elected to kick the ball out and drive from the lineout.
The decision was rewarded as captain Mpho Mbiyozo scored from a strong drive and Dukisa converted the try.
The host responded strongly and after a superb carry by big it was the turn of scrumhalf Anrich Richter to cross the tryline after straightening the line.
Kotze then converted to make it 10-10 after just 18 minutes.
Mbiyozo continued his impressive display and scored his second try for the evening after some great handling by the visitors.
Dukisa nailed the touchline conversion and the Eastern Province Kings lead 17-10 just before half-time.
The two teams went into the break with the same score and the game was still very much in the balance.
The Falcons changed their jerseys at half-time, reverting to their traditional red strip.
Fullback Wesley Roberts missed with a penalty attempt but the home team drew first blood in the second half as Kotze slotted a drop goal.
The gap was extended to seven points again after prop Nico Engelbrecht was penalised at the ruck and Dukisa kicked the penalty to make it 20-13.
The final quarter saw Dukisa kick another penalty after Wessel du Rand infringed in front of the poles.
After spreading the ball wide it was outside centre Siyanda Grey who dotted down as the Kings looked to seal the match and a possible bonus point.
Dukisa kept his perfect kicking record intact to make it 30-13 with about 15 minutes left.
This hosts tried to force their way back into the game on and Roberts intercepted a loose pass from the EP Kings to score.
Kotze missed the conversion and the Falcons still trailed by 12 point going into the final 10 minutes.
The Kings put the result beyond a doubt when captain couragous Mbiyozo completed his hat-trick after yet another strong drive and Dukisa kicked the conversion, taking the score out to 37-18.
Dukisa then collected a kick trough to score a try of his own, converting his own try to make the final score 44-18.
The Eastern Province Kings will be full of confidence going into their next clash, hosting the Border Bulldogs in Port Elizabeth.
The Falcons have the difficult task of travelling to the Pumas and will have to regroup quickly before then.
Scorers:
Falcons
Tries: Anrich Richter, Wesley Roberts
Conversions: Juan Kotze
Penalties: Juan Kotze
Drop Goal: Juan Kotze
Eastern Province Kings
Tries: Mpho Mbiyozo (3), Siyanda Grey, Ntabeni Dukisa
Conversions: Ntabeni Dukisa (5)
Penalties: Ntabeni Dukisa (3)