In a tightly contested affair, James Wilson gave Vale the lead on the 57th-minute mark when he tapped the ball home from close range.
However, Vale failed to hold on as substitute Angol's glancing header with 15 minutes to go sailed into the top corner to see Vale remain in second, two points off the top, while Bradford moved up one place to 11th.
Story of the game
In a scrappy start to the game, Bradford had the first opportunity on the quarter of an hour mark when a long ball was latched on to by former Vale man Theo Robinson, but his low drilled shot was kept out by Lucas Covolan.
Robinson was looking bright and was involved only two minutes later as his cross from the right was met by Charles Vernam but his looping header was collected by Covolan.
After having a pretty quiet start to the game, Vale did create their first flash of an opportunity when James Wilson went on a bursting run but his snapshot from the edge of the box was lashes well off target.
However, inside 21 minutes Robinson really should have made it a happy return when Vernam's cross from the left narrowly evaded the striker when really he should have got a touch to it.
Two minutes later, despite being under the cosh, it was the hosts that created the best opening of the half when room opened up for James Gibbons from range and his smashed shot was well watched and tipped over by Richard O'Donnell.
12 minutes before the break O'Donnel was called into action again as he pulled off a superb save to keep out Captain Tom Conlon's drive from distance, as he once again managed to tip it over the bar.
On the stroke of half-time, after Ben Garrity sloppily conceded possession of the ball, the Bantams on the counter-attack fed Vernam on the right and with the goal at his mercy, he really should have tested Covolan but his strike was fired wide of the near post.
After the break, the Vale came out firing and on the 57th-minute mark deservedly broke the deadlock through Wilson's seventh goal of the season.
The Valiants broke down the left and after David Amoo wriggled into the box the loose ball fell to Wilson, whose first shot was blocked by O'Donnell but he pounced quickest to poke the follow-up home.
Almost immediately after the goalscorer had left the pitch, Bradford were so close to capitalising as Paudie O'Connor's glancing header from a corner sailed narrowly past the far post.
Despite the home side looking the better, Derek Adams' side did find a leveller.
This was when a deep cross from the right from Matthew Foulds found substitute Angol unmarked and his flicked header floated into the top left-hand corner to send the visiting fans into absolute bedlam.
Then, with Bradford having gained confidence, substitute Lloyd should have won it when he was played through by Conlon, but when through on goal his low shot dribbled the wrong side of the post.
The Bantams went up the other end again on the counter-attack which ended in Elliot Watt having a go from distance but it was well held by Covolan.
The Vale were so close to grabbing a late winner as three minutes into stoppage time, a David Worrall cross was whiskers away from landing on to the toe of Conlon in the six-yard box.
Moments later, Bradford did go up the other end of the pitch and forced Covolan into another decent stop as Levi Sutton's low drive from the right was well turned behind as neither side could find that game-changing goal.
Vale not being at their usual best
Ahead of the clash, Clarke's outfit had won all of their last seven home games in all competition and had won 10 of their last 12 games.
The entertaining style of football that Vale has been playing of late and the number of goals they have been scoring has provided many fans with confidence that this season may be their time to earn promotion back to League One after having last been there in 2017.
However, this afternoon the hosts really struggled to get into their usual rhythm as for large periods they were sloppy in possession and there wasn't much quick movement off the ball.
There were not many occasions that Vale managed to get in behind Bradford's back three with the only times O'Donnell was tested was when space opened up from distance.
Despite not performing as well as they could have done, credit should still be given that they managed to come away from a point as over the last couple of seasons it could be argued that they would come away with nothing from a game like that.
That in itself should show how far the club has come since Clarke was appointed back in February and his side remain still in a healthy position to achieve their aim of automatic promotion.
Star Player- Tom Conlon
The 25-year-old has been one of the standout players for the Valiants this season and when many players failed to quite perform, Conlon was not one of them as he remained consistent and appeared to stand out once again.
He was confident when receiving the ball and tended to take it forward and take on opposition players in the midfield areas, allowing there to be space further up the pitch.
The only thing that was missing was the final ball but this was more down to the failure for electric runs off the ball instead of Conlon's sloppiness.
So far this campaign, the Vale captain has scored four and assisted four and has been a key component to everything the Valaits have done well this season up to now.