Despite playing without any substitutes or their regular keeper, Clifton's superiority was evident from the opening minute when they took the lead from a Tom Garwood header after a great passing move.
Ryan Thompson added a second before Callum Charlton got in on the act and George Gray made amends for an earlier penalty miss with a great strike from 20 yards.
Garwood added his second just before half time and Ryan Thompson bagged a sixth 10 minutes into the second half.
Despite playing with only 10 men for the last 20 minutes Clifton's dominance continued with Danny Rose latching onto a loose ball in the box to make it seven before Curtis Ioannou dribbled through the Hartshead defence to score.
The home team replied with a goal in the last minute.

BRIGHOUSE under 17s needed extra time and penalties before securing a Huddersfield Junior League Cup victory over Warley Rangers
Warley scored first but Jordan Fulton levelled from the re-start with a chip over the keeper.
Kieron Baker scored a very good second for Brighouse but Warley managed to take the lead in the second half.
Brighouse continued to be the more progressive side and gained their rewards with a good headed goal from Jack Johnstone to make it 3-3.
This took the game into extra time and penalties with Brighouse being eventual 5-4 winners.

NORTHOWRAM Rams C took on unbeaten league leaders Dewsbury C and thoroughly deserved their 3-3 draw.
Rams conceded two soft goals but that just served to rally the team.
Harris Reid won the ball in midfield and drifted past two players on the right before crossing low to his brother Kaellan, who swept it home.
The Rams poured forward again after the break but went further behind when Dewsbury scored a third.
It was not until midway through the second half that the Rams pulled another goal back, Thomas Conlon feeding Kaellan Reid who took on the last defender before knocking the ball past the keeper.
With only seconds remaining, Thomas Ketteringham collected the ball, made space and then unleashed a shot that flew into the corner of the net.
BRIGHOUSE A and Dalton Dynamoes under nines fought out an entertaining 1-1 draw.
Brighouse began brightly with Oliver Priestley-Standing working well in the middle and could have taken the lead early but Liam Read was denied.
Josh Greenwood and Sam Potter defended well although the visitors were thankful for an acrobatic save by George Widdop for keeping them level.
Brighouse took the lead when Liam Read burst free after good work from Joseph Croft and kept his cool to score.
Dalton pressed on and but for some great defending by Matthew Airey and Jonathan Wheatly the home side would have levelled. Dalton also hit a post and Widdop saved again before the home side equalised.
Liam Read and Louis Cockburn both had late chances to grab the win for the visitors but the home side held on.