Anderson, who took five wickets on his debut in the first Test, and local boy Harmison had to rely more on sweat than inspiration as Zimbabwe lost by an innings and 69 runs.
As at Lord’s last month, the touring side failed to take the game into a fourth day.
Saddled with a 322-run first-innings deficit after being skittled for 94, Zimbabwe resumed on 41 for one and hung about until deep into the final session before being dismissed for 253.
It was their ninth defeat in a row, the second-worst losing run in Test history. England, meanwhile, last won two successive games by an innings 18 years ago.
Anderson and Harmison, widely contrasting players in stature and approach, shared identical figures of four for 55 and six wickets in the match.
Debutant seamer Richard Johnson, who claimed six victims in the first innings, failed to add to that tally on Saturday.
The 20-year-old Anderson, still playing club cricket at the start of last season, has made his name for his ability to swing the ball late and at a skiddy pace.
Harmison, who plays for Durham at Chester-le-Street, relies more on throat-balls.
On Saturday, a good pitch, a cloudless sky and warm sunshine continued to favour the batsmen at the Riverside.
Anderson, leading a pace attack boasting just seven caps and 22 wickets before the second Test, responded by rolling up his sleeves and wheeling remorselessly away at a line around off stump for 23 overs.
Johnson had done just that on Friday and Anderson, showing a maturity beyond his years and experience, followed that example.
He struck early, having Stuart Carlisle (28) caught at short leg by the diving Robert Key off bat and pad after a 60-run stand with Dion Ebrahim.
Harmison then accounted for Ebrahim, who made 55 before he was trapped lbw on his crease to leave Zimbabwe lunching on 113 for three.
They needed a major innings from Grant Flower, their leading batsman, or Tatenda Taibu, a wicket-keeper masquerading as a Test match number five. Neither obliged.
Facing Anderson, Flower played on four deliveries into the afternoon for 16 while Taibu made two less before pad-batting Ashley Giles’s left-arm spin to the crouching Mark Butcher at silly mid-off.
Zimbabwe’s lower order looked almost a match for the batsmen who had gone before as Sean Ervine and Travis Friend, who made 65 not out, hinted at a fourth day’s play.
They relied on straight and powerful strokes during a 70-ball half-century partnership for the sixth wicket, Ervine lofting Giles over long on and hitting the next ball in the same direction for four.
Ervine, however, on 34, played back to a trademark Harmison lifter and chopped the ball into his stumps to make it 185 for six.
Zimbabwe’s wretched series was summed up by captain Heath Streak’s dismissal just before tea.
Friend drove a return catch to Harmison who dropped the chance but somehow helped the ball into the stumps at the non-striker’s end with Streak out of the crease.
The final session was chiefly memorable for a Nasser Hussain catch and for the crowd’s delight at the end of a pitifully short and one-sided series. The England captain, in his one meaningful contribution to the series, dived full length running from mid-on to pouch Andy Blignaut off Anderson.
Scoreboard
ENGLAND (1st Innings) 416 (A. McGrath 81, A.J. Stewart 68, A.F. Giles 50; H.H. Streak 4-64).
ZIMBABWE (1st Innings) 94 (R.L. Johnson 6-33).
ZIMBABWE (2nd Innings, overnight 41-1):
D.D. Ebrahim lbw b Harmison 55
M.A. Vermeulen c McGrath b Anderson 0
S.V. Carlisle c Key b Anderson 28
G.W. Flower b Anderson 16
T. Taibu c Butcher b Giles 14
S.M. Ervine b Harmison 34
T.J. Friend not out 65
H.H. Streak run out 3
A.M. Blignaut c Hussain b Anderson 12
R.W. Price c Stewart b Harmison 6
D.T. Hondo b Harmison 4
EXTRAS (B-6, LB-10) 16
TOTAL (all out, 93.4 overs) 253
FALL OF WKTS: 1-5, 2-65, 3-102, 4-113, 5-131, 6-185, 7-202, 8-223, 9-244.
BOWLING: Anderson 23-8-55-4; Johnson 22-7-67-0; Harmison 21.4-4-55-4; Giles 25-9-51-1; Butcher 2-0-9-0.
RESULT: England won by an innings and 69 runs (England win two-match series 2-0).
UMPIRES: D.B. Hair (Australia) and D.L. Orchard (South Africa).
TV UMPIRE: P. Willey (England).
MATCH REFEREE: C.H. Lloyd (West Indies).
FIRST TEST: Lord’s, England won by an innings and 92 runs.—Reuters