The home side were hampered by the second-half dismissal of star centre Ryan Lonsdale but, had they taken their chances early in the game, they would have been celebrating a great victory.
Malton’s early pressure had Beverley in trouble, but the visitors managed to keep their line intact. Against the run of play, Beverley took the lead on 12 minutes with a penalty from fly-half Phil Dubouley when Malton were penalised for a high tackle.
Seven minutes later, Beverley were penalised for a similar offence but Ian Cooke’s effort sailed wide. Malton suffered a hammer blow when Lonsdale was sin-binned for a dangerous tackle and the visitors used the extra man to put wing Tamasai Tanumi over in the corner.
Pressure in the set scrum brought a penalty which Cooke converted to make it 8-3 to Beverley at half-time.
Malt reduced the arrears with another Cooke penalty three minutes into the second half. On 46 minutes, the hosts took the lead when Tom Newitt fed fly-half Chris Creber and his pass gave Lonsdale the room to power over. Cooke converted for a 13-8 lead.
However, ten minutes into the half, Lonsdale received a second yellow card, and subsequent red, for another high tackle.
The home defence held out for 20 minutes under immense pressure, but Beverley finally found the extra room to get wing Goran Jelencic across the line. Duboulay added the conversion.
With the game deep into injury time, Beverley skipper Junior Tupai crossed for the final score.
Pocklington were left reflecting on another home game they should have won with something to spare after they handed visitors Morley a 25-20 victory.
Morley arrived at Percy Road on the back of an eight-match winning run that has put them in the promotion frame.
But Pocklington outplayed their visitors for much of the first half and should have gone in at the break with a bigger lead than their 10-8 advantage.
The hosts scored two tries, from flanker Jack Holbrough and lock Dan Wilson, who both raced over from 20 yards.
Pock's big problem was their goal kicking. Without top marksman Nick Bennett due to work commitments, they tried three different kickers but missed four penalties and two conversions.
Morley played the percentages and took their chances to build an 18-10 lead midway through the second half.
Third choice kicker Jack Fletcher finally hit the target with a penalty from in front of the posts, but Pock then gifted Morley a fourth try from a charged down kick.
From the last play of the game, replacement back Pete Massie glided down the right touchline before finding Wilson on his inside to race clear for his second score.
Fletcher converted to ensure that Pocklington at least came away with a losing bonus point.
Meanwhile, York cemented their place in Yorkshire One’s top five with a 29-24 win at sixth-placed North Ribblesdale.
The home side opened the scoring with a converted try, but York responded on 32 minutes when hooker Freddie Potrykus sent Mark Benson over for a try.
Benson crossed again two minutes before the break after good work by Joe Maud, Andy Kay and Willem Enslin and York led 10-7 at half-time.
Two quick tries after the interval put York in charge at 22-7 in front, with James Hartley crossing and Matt Dudman converting before, from the restart, the visitors broke and Ben Hepworth scorched over after a flowing move.
A converted try on 53 minutes followed by a penalty saw the hosts pull back to 22-17, but York conjured a try by Andy Kay, which Dudman converted.
A late Ribblesdale try made for a tense finale, but York managed to hang on to extend their unbeaten run to nine league and cup games. They are now seven points clear of Saturday’s beaten hosts.
York RI are 25 points from safety in Yorkshire Three after a 24-17 defeat by third-from-bottom Northallerton at New Lane.