Beattie, enjoying his first taste of this fixture, slipped a first-half strike through the legs of Graham Stack following a sensational Ian Black cross-field pass.
Late substitute Santana added some gloss to the result, with a splendid individual goal, darting from the halfway line before curling a fine effort past Stack.
The lacklustre visitors' best chances came through Matt Doherty in the second period.
The result leaves the Easter Road outfit still without a win in three years in this fixture, and does nothing to ease Hibs' relegation worries as they remain just four points ahead of Dunfermline at the foot of the Clydesdale Bank Premier League.
Hearts remain sixth in the standings, but have moved to within one point of St Johnstone and Dundee United in the chase for Europa League football.
The home side showed three changes from the side which drew 2-2 win St Mirren in the William Hill Scottish Cup last weekend.
Darren Barr replaced Marius Zaliukas and Jamie Hamill came in for Ryan McGowan. Meanwhile, Jambos top-scorer with 10 goals Rudi Skacel was drafted in for Adrian Mrowiec.
Tom Soares and David Wotherspoon were brought in by Hibs to replace suspended duo Ivan Sproule and Isaiah Osbourne in the only two changes from the 2-0 win over Ayr.
Pat Fenlon's side included six players making their Edinburgh derby debut, with George Francomb, James McPake, Pa Kujabi, Jorge Claros and Roy O'Donovan joining Soares for this tempestuous fixture.
The first incident of note was fittingly physical, with a clash of heads between Francomb and Skacel leaving both dazed and the latter with a head wound.
Yet it was Francomb who clearly came off worse, having to be replaced by Matt Doherty.
It took 13 minutes for the first real opportunity, with Soares diverting a wicked Ian Black delivery a matter of inches over his own crossbar.
A wayward Beattie effort followed, heading wide from a Driver cross.
With the hosts in the ascendancy, Graham Stack was forced into action. The former Arsenal trainee fisted away a towering header from stand-in skipper Webster, following a super Danny Grainger corner.
Against the run of play, Hibs could have claimed the lead with the half-hour mark approaching.
Some nice interplay between the previously quiet Leigh Griffiths and Pa Kujabi set the Gambian left-back free inside the box. His delivery across the face of goal was tantalising but there were no takers.
And seconds later Fenlon's men were behind. A stunning 50-yard diagonal ball from Black set Beattie through on goal and the former Celtic striker held off the challenge of Doherty brilliantly before sliding a low effort past Stack.
Beattie, a constant nuisance to the Hibs backline, volleyed over the bar just before half-time after a long Skacel clearance was inadequately headed away by Paul Hanlon.
Hibs emerged with more vigour after the break, and Matt Doherty saw two headers - within seconds of each other - cleared off the line, with Beattie, then Driver, in the right place at the right time.
With less than 20 minutes to play Griffiths wasted a decent chance for the Easter Road outfit. From a nicely placed free-kick from 25 yards the Scotland under-21 international fired wastefully over the bar.
Five minutes later Hibs should have been level. Griffiths delivered a sumptuous clipped cross into the box but, from point-blank range, Roy O'Donovan's glancing header was saved by the legs of Jamie MacDonald.
It would prove to be the last chance for Fenlon's men, and it was Hearts who would end the game in style.
Santana, on as a late replacement for Skacel, picked up the ball on halfway, danced past two challenges on his way to the box and curled a delightful effort past Stack.