Mido scored the winner for Tottenham in a 3-2 victory over Blackburn in the English Premier League on Sunday.
In Sunday's other match, Georgios Samaras scored twice in as many minutes for Manchester City in a 2-1 win over bottom club Sunderland.
Spurs is five points from third-place Manchester United and five points clear of fifth-place north London rival Arsenal. Blackburn stays in sixth, one point behind the Gunners.
The top four clubs in England qualify for the Champions League. The only time Tottenham has played Europe's top club competition was when it reached the semifinals of the European Cup in 1962.
At White Hart Lane, Keane scored in the ninth and 22nd minutes. Blackburn pulled a goal back through Florent Sinama Pongolle in the 44th and leveled with Craig Bellamy's goal in the 67th.
At the Manchester City of Manchester Stadium, Samaras scored in the ninth and tenth minutes, five days after making his international debut for Greece with a goal in a 1-0 friendly win over Belarus.
"Georgios has a very bright future at this club," Manchester City manager Stuart Pearce said of the 21-year-old, who joined in January from Dutch club Heerenveen.
"From day one, I have been really impressed with his willingness to learn and felt he was someone I wanted to work with for the next few years."
Kevin Kyle pulled a goal back for Sunderland in the 25th, but it wasn't enough to stop Sunderland from losing its 22nd game of the season. The club is at the bottom of the standings and almost certain to be relegated.
Sunderland is 16 points adrift of safety and needs nine points from its final 10 games to avoid becoming the worst side in Premier League history.
Sunderland captain Gary Breen was sent off in the 85th minute for a second yellow card.
"My only target for the rest of the season is to get as many points as we can," Sunderland manager Mick McCarthy said. "We have to keep scrapping away and we have to stop gifting the opposition stupid goals, which stop us even having a chance of winning."
Manchester City started US captain Claudio Reyna for the first time since Dec. 26 after he recovered from surgery on his right ankle.
Chelsea has 72 points, followed by Liverpool's 55, Manchester United with 54, Tottenham on 49 and Arsenal with 44.
Roman Bednar scored the winner for Hearts in a 3-2 victory over Livingston.
Hearts twice took the lead only for Livingston to level each time before Bednar's decider in the 87th minute. Bruno Aguiar and Edgaras Jankauskas also scored for Hearts, with Richard Brittain and David Mackay netting for Livingston.
Hearts stayed second, 13 points behind leader Celtic. Livingston is at the bottom of the standings. The club's 20th loss was the first match in charge for John Robertson.
"It was very difficult. We managed to get the lead twice and they came back into it both times," Hearts defender Andy Webster said. "They showed a good fighting spirit but their manager has probably instilled that in them.
"It was a big game for us and we are delighted to come away with three points. They worked hard and made us defend, so we were happy with the win."
Valencia drew 0-0 with last-place Malaga, remaining in third place and slipping 10 points behind leader FC Barcelona.
Valencia extended its unbeaten run to 15 games, but its failure to win its last two matches has hit its hopes of winning a third title in five seasons.
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