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Spurs' victory consolidated their hold on fourth place and kept them on target for a Champions League spot, while Portsmouth missed a chance to breathe life into their faint hopes of avoiding relegation from the English Premier League.
England striker Crouch headed the opener in the 27th minute while Croatia midfielder Kranjcar flicked in the second in the 41st minute in the warm-up for the FA Cup semi-final between the two sides at Wembley on April 11.
As Spurs cruised to their fifth league win in a row, Portsmouth - already missing several key players through injury - were left to count the cost as defender Hermann Hreidarsson and striker Danny Webber were stretchered off and goalkeeper captain David James also came off injured.
Portsmouth had the better of the opening exchanges, though goalkeeper Heurelho Gomes was untroubled by two wayward efforts from Anthony Vanden Borre and an early Nwankwo Kanu drive.
Eidur Gudjohnsen, on loan to Spurs from Monaco, sent a seventh minute header over James's crossbar. His strike partner Crouch then sent another header wide.
Gomes was then forced into an excellent save after a flowing move from the visitors. Frederic Piquionne played an excellent through-ball for Vanden Borre, but the Brazilian came rushing out to block the shot.
At the other end, England goalkeeper James was grateful when the ball fell right into his arms after a cross from Kyle Walker, on his Spurs debut, came off Hayden Mullins as he got to it ahead of Kranjcar.
But within minutes, the Croatian crossed the ball into the penalty box for Crouch to score.
The forward got the better of South Africa's Aaron Mokoena, playing at centre-half, to head past James.
Spurs captain Michael Dawson could have made it 2-0 three minutes later but the defender's powerful header from a David Bentley cross went wide.
Spurs then went close to scoring three times in a minute as they laid siege to Pompey's goal.
First midfielder Tom Huddlestone blasted a left-foot shot against the crossbar, then Crouch crashed a right-foot volley against the far post in the same move.
He then attempted an over-head kick but it went straight at James, much to Pompey's relief.
But Spurs did not have to wait much longer for their second goal.
Portsmouth failed to clear a Mullins shot and Kranjcar knocked a simple, backheeled flick into the net in the 41st minute.
The misery continued for Pompey straight after the break when Hreidarsson was stretchered off, having fallen heavily and injured his left ankle. Webber was brought on to replace him.
The visitors then went on the attack and fashioned some half-chances before Kanu sent a 58th-minute shot at Gomes and a Michael Brown blast went wide.
Dawson walked off injured in the 61st minute as Pompey kept up their attacking drive, though Gomes was given little to do.
James did well to save a low Sebastien Bassong header from a Bentley corner with 10 minutes to go.
Webber was stretchered off with three minutes to go, and James came off in the 89th minute.
Crouch put an injury-time chance wide but he had done more than enough to dampen Pompey's spirits ahead of their FA Cup clash.
