Manchester City reject Joe Hart produced three terrific saves to deny Roman Bezjak, Josip Ilicic and Jasmin Kurtic, who also hit the post, as Gareth Southgate's inexperienced side clung on desperately for a point in Ljubljana to remain top of Group F.
Jesse Lingard's fierce long-range strike forced Slovenia goalkeeper Jan Oblak into a sharp stop late on as the stalemate ensured both countries maintained their unbeaten starts to the campaign.
"It's my best game for a while but it was down to a few errors from us," said Hart, who kept a third successive clean sheet in qualifying.
"We have to improve but we are trying to qualify for Russia. My body is in pieces, I'll struggle to get up tomorrow," added Hart, who has been shunted out on loan to Torino in Serie A.
England moved on to seven points after three matches, two more than Slovenia and Lithuania, who defeated 10-man Malta 2-0 in Vilnius.
Slovakia registered their first points with a commanding 3-0 victory over Scotland in Trnava where Robert Mak scored twice before Adam Nemec capped off a miserable evening for Gordon Strachan's visitors.
In Hanover, defending champions Germany swept aside Northern Ireland 2-0 with first-half goals from Julian Draxler and Sami Khedira sending Joachim Loew's men two points clear in Group C and looking ominous.
"We've done our job, taking six points (this past week) and not conceding any goals," said Loew. "We scored our two goals very early and that allowed us to win without suffering."
Azerbaijan extended their undefeated run with a hard-fought point in a goalless draw in the Czech Republic, Robert Prosinecki's team a surprise second in the standings following their shock defeat of Norway at the weekend.
The Norwegians were in danger of another highly embarrassing result at home to San Marino before three goals in the final 13 minutes eased tensions in Oslo as the hosts won 4-1.
Robert Lewandowski snatched a dramatic stoppage-time winner as Poland overcome 10-man Armenia 2-1 in Warsaw.
Hrayr Mkoyan's own goal just after the break gifted Poland the lead, but Armenia, who played a man down for an hour after the dismissal of Gael Andonian, levelled two minutes later through Marcos Pizzelli.
However, Lewandowski scored for the eighth straight qualifier as he headed in deep into injury time to keep Poland level on points with Group E leaders Montenegro, 1-0 winners in Denmark.
Romania are two points off the pace following a 0-0 draw with Kazakhstan in Astana.