But that ranking is misleading as Przysiezny, who has a good Davis Cup pedigree, was a top 200-ranked player before a lengthy injury-enforced lay-off, and the way the match developed highlighted just how false the world standings were.
He broke Evans to love in the fourth game of the first set and the Englishman struggled to deal with his serve as Przysiezny dominated a one-sided first set.
GB captain John Lloyd did his best to try and keep up Evans's visibly faltering morale, but it was to little effect.
Evans's fourth double fault put Przysiezny 5-1 up, and he duly served out for the second set - but taking charge of the game seemed to break Przysiezny's concentration, and inspired a mini-Evans revival.
He had the Liverpool crowd on their feet with two breaks of serve in the third set but his comeback was snuffed out when Przysiezny broke back to cut the deficit to 4-3 with a beautifully judged drop shot.
Lloyd 'realistic' after Davis Cup relegation
From therein, the Polish number two gathered his concentration and was efficient in the way he wrapped up victory.
Earlier on, Murray made light of a wrist injury to play his third match in as many days, a victory which raised British hopes.
After breaking his opponent in the fourth game for a 3-1 lead, Murray's stiffest test of the first set came in the seventh game, which was won when Janowicz put a return wide.
A clearly-fired up Murray went on to take the opening set 6-3, clinching it with a delightfully under-hit shot from the baseline which caught out the Pole who sprinted up to the net just too late to reach it.
In the second set, Janowicz did well to hold his serve after five deuces but was broken to love in his next service game, giving Murray a vital 3-2 lead.
The world number three was carrying a wrist injury and admitted he was only playing because it was the Davis Cup, and was clearly in a hurry to get the job done.
Janowicz showed plenty of nice touches but once Murray secured the second set, there was little chance of an upset.
Highlights - Murray too strong for Janowicz (UK only)
A delightful cushioned, angled shot clinched a break for Murray in the opening game of the third set, which he followed by holding his serve to love.
The Pole had two break points in Murray's next service game, but once the Scot survived that test, the momentum was clearly with him and his victory was never in serious doubt.
Towards the end he really began to turn on the style, particularly with his shots from the back of the court, and Murray eventually wrapped up victory in just under two hours.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.